Injection drug use is one of the most significant risk factors associated with contracting human immunodeficiency virus (HIV), and drug users infected with HIV suffer from a higher viral load and rapid disease progression. While replication of HIV may result in many mutant viruses that can escape recognition of the host's immune response, the presence of morphine (a drug of abuse) can decrease the viral mutation rate and cellular immune responses. This study develops a mathematical model to explore the effects of morphine-altered mutation and cellular immune response on the within-host dynamics of two HIV species, a wild-type and a mutant. Our model predicts that the morphine-altered mutation rate and cellular immune response allow the wild-type virus to out-compete the mutant virus, resulting in a higher set point viral load and lower CD4 count. We also compute the basic reproduction numbers and show that the dominant species is determined by morphine concentration, with the mutant dominating below and the wild-type dominating above a threshold. Furthermore, we identified three biologically relevant equilibria, infection-free, mutant-only, and coexistence, which are completely characterized by the fitness cost of mutation, mutant escape rate, and morphine concentration.

This paper presents a mathematical model capable to reproduce a celebrated phenomenon in blood microcirculation known as Fåhræus effect, since its discovery by Robin Fåhræus (1929). This consists in a decaying of the relative hematocrit in small vessels as the vessel diameter decreases. The key point of the model is a formula, direct consequence of the basic principles of fluid dynamics, that links the relative hematocrit to the reservoir hematocrit and the vessel diameter, which confirms the observed behavior. To test the model we selected, among the few experiments carried on since then, those performed by Barbee and Cokelet (1971). The agreement is remarkable. An extended comparison is also carried out with a celebrated empirical formula proposed by Pries et al. (1992) to describe the same phenomenon.

This study explores infectious disease transmission through contact during daily trips between municipalities. We propose an extended susceptible-infectious-recovered model that considers daily movements on the spatial spread of infectious disease. The current model considers two types of movement: long-term movements such as migration and shorter activities completed within a day. We present analytical results using a next-generation matrix and numerical results using actual human flow data, focusing on the number of days it takes for an outbreak from each region to reach the entire area. Our results suggest that the likelihood of infection depends on the ratio of human flow to population rather than the population per se.

The novel coronavirus SARS-CoV-2 emerged in 2019 and subsequently spread throughout the world, causing over 600 million cases and 6 million deaths as of September 7th, 2022. Superspreading events (SSEs), defined here as public or social events that result in multiple infections over a short time span, have contributed to SARS-CoV-2 spread. In this work, we compare the dynamics of SSE-dominated SARS-CoV-2 outbreaks, defined here as outbreaks with relatively higher SSE rates, to the dynamics of non-SSE-dominated SARS-CoV-2 outbreaks. To accomplish this, we derive a continuous-time Markov chain (CTMC) SARS-CoV-2 model from an ordinary differential equation (ODE) SARS-CoV-2 model and incorporate SSEs using an events-based framework. We simulate our model under multiple scenarios using Gillespie's direct algorithm. The first scenario excludes hospitalization and quarantine; the second scenario includes hospitalization, quarantine, premature hospital discharge, and quarantine violation; and the third scenario includes hospitalization and quarantine but excludes premature hospital discharge and quarantine violation. We also vary quarantine violation rates. Results indicate that, with either no control or imperfect control, SSE-dominated outbreaks are more variable but less severe than non-SSE-dominated outbreaks, though the most severe SSE-dominated outbreaks are more severe than the most severe non-SSE-dominated outbreaks. We measure severity by the time it takes for 50 active infections to be achieved; more severe outbreaks do so more quickly. SSE-dominated outbreaks are also more sensitive to control measures, with premature hospital discharge and quarantine violation substantially reducing control measure effectiveness.

The coronavirus (SARS-CoV-2) exhibited waves of infection in 2020 and 2021 in Japan. The number of infected had multiple distinct peaks at intervals of several months. One possible process causing these waves of infection is people switching their activities in response to the prevalence of infection. In this paper, we present a simple model for the coupling of social and epidemiological dynamics. The assumptions are as follows. Each person switches between active and restrained states. Active people move more often to crowded areas, interact with each other, and suffer a higher rate of infection than people in the restrained state. The rate of transition from restrained to active states is enhanced by the fraction of currently active people (conformity), whereas the rate of backward transition is enhanced by the abundance of infected people (risk avoidance). The model may show transient or sustained oscillations, initial-condition dependence, and various bifurcations. The infection is maintained at a low level if the recovery rate is between the maximum and minimum levels of the force of infection. In addition, waves of infection may emerge instead of converging to the stationary abundance of infected people if both conformity and risk avoidance of people are strong.

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.

The recent discovery that some terrestrial arthropods can detect, use, and learn from weak electrical fields adds a new dimension to our understanding of how organisms explore and interact with their environments. For bees and spiders, the filiform mechanosensory systems enable this novel sensory modality by carrying electric charge and deflecting in response to electrical fields. This mode of information acquisition opens avenues for previously unrealised sensory dynamics and capabilities. In this paper, we study one such potential: the possibility for an arthropod to locate electrically charged objects. We begin by illustrating how electrostatic interactions between hairs and surrounding electrical fields enable the process of location detection. After which we examine three scenarios: (1) the determination of the location and magnitude of multiple point charges through a single observation, (2) the learning of electrical and mechanical sensor properties and the characteristics of an electrical field through several observations, (3) the possibility that an observer can infer their location and orientation in a fixed and known electrical field (akin to "stellar navigation"). To conclude, we discuss the potential of electroreception to endow an animal with thus far unappreciated sensory capabilities, such as the mapping of electrical environments. Electroreception by terrestrial arthropods offers a renewed understanding of the sensory processes carried out by filiform hairs, adding to aero-acoustic sensing and opening up the possibility of new emergent collective dynamics and information acquisition by distributed hair sensors.

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number, Rt. Real-time or retrospective identification of changes in Rt following the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts in Rt within a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume that Rt is piecewise-constant, and the incidence data and priors determine when or whether Rt should change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty in Rt and its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where the Rt profile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The proportion of SARS-CoV-2 infections ascertained through healthcare and community testing is generally unknown and expected to vary depending on natural factors and changes in test-seeking behaviour. Here we use population surveillance data and reported daily case numbers in the United Kingdom to estimate the rate of case ascertainment. We mathematically describe the relationship between the ascertainment rate, the daily number of reported cases, population prevalence, and the sensitivity of PCR and Lateral Flow tests as a function time since exposure. Applying this model to the data, we estimate that 20%-40% of SARS-CoV-2 infections in the UK were ascertained with a positive test with results varying by time and region. Cases of the Alpha variant were ascertained at a higher rate than the wild type variants circulating in the early pandemic, and higher again for the Delta variant and Omicron BA.1 sub-lineage, but lower for the BA.2 sub-lineage. Case ascertainment was higher in adults than in children. We further estimate the daily number of infections and compare this to mortality data to estimate that the infection fatality rate increased by a factor of 3 during the period dominated by the Alpha variant, and declined in line with the distribution of vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Bayesian inference produces a posterior distribution for the parameters of a mathematical model that can be used to guide the formation of hypotheses; specifically, the posterior may be searched for evidence of alternative model hypotheses, which serves as a starting point for hypothesis formation and model refinement. Previous approaches to search for this evidence are largely qualitative and unsystematic; further, demonstrations of these approaches typically stop at hypothesis formation, leaving the questions they raise unanswered. Here, we introduce a Kullback-Leibler (KL) divergence-based ranking to expedite Bayesian hypothesis formation and investigate the hypotheses it generates, ultimately generating novel, biologically significant insights. Our approach uses KL divergence to rank parameters by how much information they gain from experimental data. Subsequently, rather than searching all model parameters at random, we use this ranking to prioritize examining the posteriors of the parameters that gained the most information from the data for evidence of alternative model hypotheses. We test our approach with two examples, which showcase the ability of our approach to systematically uncover different types of alternative hypothesis evidence. First, we test our KL divergence ranking on an established example of Bayesian hypothesis formation. Our top-ranked parameter matches the one previously identified to produce alternative hypotheses. In the second example, we apply our ranking in a novel study of a computational model of prolactin-induced JAK2-STAT5 signaling, a pathway that mediates beta cell proliferation. Within the top 3 ranked parameters (out of 33), we find a bimodal posterior revealing two possible ranges for the prolactin receptor degradation rate. We go on to refine the model, incorporating new data and determining which degradation rate is most plausible. Overall, while the effectiveness of our approach depends on having a properly formulated prior and on the form of the posterior distribution, we demonstrate that our approach offers a novel and generalizable quantitative framework for Bayesian hypothesis formation and use it to produce a novel, biologically-significant insight into beta cell signaling.

Head-tail planaria morphologies are influenced by the electric potential differences across the animal's primary axis, as evidenced e.g. by voltage-sensitive dyes and functional experiments that create permanent lines of 2-headed but genetically wild-type animals. However, bioelectrical and biochemical models that make predictions on what would happen in the case of spatial chimeras made by tissue transplantation from different planaria (different species and head shapes) are lacking. Here, we use a bioelectrical model to qualitatively describe the effects of tissue transplantation on the shape of the regenerated head. To this end, we assume that the cells may have distinct sets of ion channels and ascribe the system outcome to the axial distributions of average cell potentials over morphologically relevant regions. Our rationale is that the distributions of signaling ions and molecules are spatially coupled with multicellular electric potentials. Thus, long-time downstream transcriptional events should be triggered by short-time bioelectrical processes. We show that relatively small differences between the ion channel characteristics of the cells could eventually give noticeable changes in the electric potential profiles and the expected morphological deviations, which suggests that small but timely bioelectrical actions may have significant morphological effects. Our approach is based on the observed relationships between bioelectrical regionalization and biochemical gradients in body-plan studies. Such models are relevant to regenerative, developmental, and cancer biology in which cells with distinct properties and morphogenetic target states confront each other in the same tissue.

Metabolism is essential for cell function and adaptation. Because of their central role in metabolism, kinetic parameters and enzyme concentrations are under constant selective pressure to adapt the fluxes of the metabolic networks to the needs of the organism. In line with various studies dealing with enzyme evolution, we recently developed a model of the evolution of enzyme concentrations under selection for increased flux, considered as a proxy for fitness (Coton et al., 2022). With this model, taking into account two realistic cellular constraints, competition for resources and co-regulation, we determined the evolutionary equilibria and range of neutral variations of enzyme concentrations. In this article, we expanded this model by considering that the enzymes in a pathway can belong to different co-regulation groups. We determined the equilibria and showed that the constraints modify the adaptive landscape by limiting the number of independent dimensions. We also showed that any trade-off between enzyme concentrations is sufficient to limit the flux and relax selection for increasing the concentration of other enzymes. Even though this model is based on simplifying assumptions, the complexity of the relationship between enzyme concentrations prevents the formal analysis of the range of neutral variation of enzyme concentrations. However, we could show that selection for maximizing the flux results in selective neutrality for all enzymes regardless the constraints applied, giving generality to the prediction of Hartl et al. (1985).

During the SARS-CoV-2 pandemic, epidemic models have been central to policy-making. Public health responses have been shaped by model-based projections and inferences, especially related to the impact of various non-pharmaceutical interventions. Accompanying this has been increased scrutiny over model performance, model assumptions, and the way that uncertainty is incorporated and presented. Here we consider a population-level model, focusing on how distributions representing host infectiousness and the infection-to-death times are modelled, and particularly on the impact of inferred epidemic characteristics if these distributions are mis-specified. We introduce an SIR-type model with the infected population structured by 'infected age', i.e. the number of days since first being infected, a formulation that enables distributions to be incorporated that are consistent with clinical data. We show that inference based on simpler models without infected age, which implicitly mis-specify these distributions, leads to substantial errors in inferred quantities relevant to policy-making, such as the reproduction number and the impact of interventions. We consider uncertainty quantification via a Bayesian approach, implementing this for both synthetic and real data focusing on UK data in the period 15 Feb-14 Jul 2020, and emphasising circumstances where it is misleading to neglect uncertainty. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Detection of extremely rare variant alleles, such as tumor DNA, within a complex mixture of DNA molecules is experimentally challenging due to sequencing errors. Barcoding of target DNA molecules in library construction for next-generation sequencing provides a way to identify and bioinformatically remove polymerase induced errors. During the barcoding procedure involving t consecutive PCR cycles, the DNA molecules become barcoded by Unique Molecular Identifiers (UMIs). Different library construction protocols utilize different values of t. The effect of a larger t and imperfect PCR amplifications in relation to UMI cluster sizes is poorly described. This paper proposes a branching process with growing immigration as a model describing the random outcome of t cycles of PCR barcoding. Our model discriminates between five different amplification rates r1, r2, r3, r4, r for different types of molecules associated with the PCR barcoding procedure. We study this model by focussing on Ct, the number of clusters of molecules sharing the same UMI, as well as Ct(m), the number of UMI clusters of size m. Our main finding is a remarkable asymptotic pattern valid for moderately large t. It turns out that E(Ct(m))/E(Ct)≈2-m for m=1,2,…, regardless of the underlying parameters (r1,r2,r3,r4,r). The knowledge of the quantities Ct and Ct(m) as functions of the experimental parameters t and (r1,r2,r3,r4,r) will help the users to draw more adequate conclusions from the outcomes of different sequencing protocols.

A spatially-distributed continuous mathematical model of solid tumor growth and treatment by fractionated radiotherapy is presented. The model explicitly accounts for the factors, widely referred to as 4 R's of radiobiology, which influence the efficacy of radiotherapy fractionation protocols: tumor cell repopulation, their redistribution in cell cycle, reoxygenation and repair of sublethal damage of both tumor and normal tissues. With the use of special algorithm the fractionation protocols that provide increased tumor control probability, compared to standard clinical protocol, are found for various physiologically-based values of model parameters under the constraints of fixed overall normal tissue damage and maximum admissible fractional dose. In particular, it is shown that significant gain in treatment efficacy can be achieved for tumors of low malignancy by the use of protracted hyperfractionated protocols. The optimized non-uniform protocols are characterized by gradual escalation of fractional doses in their last parts, which start after the levels of oxygen and nutrients significantly elevate throughout the tumor and accelerated tumor proliferation manifests itself, which is a well-known experimental phenomenon.

The mechanical properties of limb long bones are impacted by bone shape and especially curvature, which is therefore likely to be of adaptive value. We use finite element analysis to compare the mechanical properties of humeri of the closely related American otter and honey badger under external loads, and to analyze the significance of bone curvature. We simulate the effects generated by loads applied in directions that differ relative to the humeral longitudinal axes, and then compare the stress characteristics with a series of humerus-inspired abstracted curved structures with increasing ratio (C/R) of eccentricity C to radius of cross section R. The humeri of the two species differ in bone curvature, with C/R of 0.6201 and 0.8752, respectively. Our analysis shows that the peak and mean stress values found within the sampling line of bone models reach a minimum when the directions of loads are 105 ± 5°, and the humerus of the American otter always experienced lower stress values than those of the honey badger in the sampling line. An analysis of stress distribution in abstract curved structures showed the greatest reduction in stress when the direction of external load was equal or greater than 95°. This suggests that the variability of the direction of external loads is an important determinant of bone curvature, and should be accounted for when assessing load carrying capacity. This study provides a basis for biomechanics research and yields insight into the form-function relationship of nature's structural elements within limbs. It potentially contributes to the design of biomimetic robots while also highlighting the functional significance of humeral bone curvature in mammals.

SARS-CoV-2 (SARS2) regularly mutates resulting to variants of concern (VOC) which have higher virulence and transmissibility rates while concurrently evading available therapeutic strategies. This highlights the importance of amino acid mutations occurring in the SARS2 spike protein structure since it may affect virus biology. However, this was never fully elucidated. Here, network analysis was performed based on the COVID-19 genomic epidemiology network between December 2019-July 2021. Representative SARS2 VOC spike protein models were generated and quality checked, protein model superimposition was done, and common contact based on contact mapping was established. Throughout this study, we found that: (1) certain individual variant-specific amino acid mutations can affect the spike protein structural pattern; (2) certain individual variant-specific amino acid mutations had no affect on the spike protein structural pattern; and (3) certain combination of variant-specific amino acids are putatively epistatic mutations that can potentially influence the VOC spike protein structural pattern. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

We numerically study the role of excitatory and inhibitory interactions in the aggregations of male frogs. In most frogs, males produce sounds to attract conspecific females, which activates the calling behavior of other males and results in collective choruses. While the calling behavior is effective for mate attraction, it requires high energy consumption. In contrast, satellite behavior is an alternative mating strategy in which males deliberately stay silent in the vicinity of a calling male and attempt to intercept the female attracted to the caller, allowing the satellite males to reduce their energy consumption while having a chance of mating. Here we propose a hybrid dynamical model in which male frogs autonomously switch among three behavioral states (i.e., calling state, resting state, and satellite state) due to the excitatory and inhibitory interactions. Numerical simulations of the proposed model demonstrated that (1) both collective choruses and satellite behavior can be reproduced and (2) the satellite males can prolong the energy depletion time of the whole aggregation while they split the maximum chorus activity into two levels over the whole chorusing period. This study highlights the importance of the multiple behavioral types and their transitions for the performance of the whole aggregation.

Neutral theory predicts that the genetic diversity within a population is proportional to the effective population size. In contrast, the observed genetic diversity for various species vary in a narrow range for several orders of magnitude change in the population sizes (Lewontin's paradox). The selective sweeps and background selection, reduce the genetic variation at the linked neutral sites and have been studied considering the environment to be selectively constant. However, in a natural population, the selective environment varies with time. Here, we investigate the impact of selective sweeps and background selection on neutral genetic diversity when the selection coefficient changes periodically over time. The reduction in genetic variation due to selective sweeps is known to depend on the conditional fixation time. Here, we find that the effect of changing environment on conditional mean fixation time is most substantial for the randomly mating population than the inbreeding population with arbitrary inbreeding coefficient. We also study the effect of background selection on neutral sites when the selection coefficient of linked deleterious mutation change periodically in time. In the slowly changing environment, we find that neutral heterozygosity is significantly different, and the site frequency spectrum has a different shape than that in the static environment.

Explaining the emergence of diversity and the coexistence of competing types has long been one of the main goals of ecological theory. Rugged fitness landscapes have often been used to explain diversity through the presence of local peaks, or adaptive zones, in the fitness landscape acting as available niches for different species. Alternatively, niche-packing and theories based on limiting similarity describe frequency-dependent selection leading to the organic differentiation of a continuous phenotype space into multiple coexisting types. By combining rugged carrying capacity landscapes with frequency-dependent selection, here we investigate the effects of ruggedness on adaptive diversification and stably maintained diversity. We show that while increased ruggedness often leads to a decreased opportunity for adaptive diversification, it is the shape of the global carrying capacity function, not the local ruggedness, that determines the diversity of the ESS and the total diversity a system can stably maintain.

We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves. The model, as shown by numerical simulations, captures both the time-evolution of the tumor growth before and after angiogenesis and its spatial properties, with different distribution of proliferating and hypoxic cells in the external and deep layers of the tumor, and the spatial structure of the angiogenic network. The microscopic description of the growth opens the possibility of tuning the model to patient-specific scenarios.

Conformist and anti-conformist cultural transmission have been studied both empirically, in several species, and theoretically, with population genetic models. Building upon standard, infinite-population models (IPMs) of conformity, we introduce finite-population models (FPMs) and study them via simulation and a diffusion approximation. In previous IPMs of conformity, offspring observe the variants of n adult role models, where n is often three. Numerical simulations show that while the short-term behavior of the FPM with n=3 role models is well approximated by the IPM, stable polymorphic equilibria of the IPM become effective equilibria of the FPM at which the variation persists prior to fixation or loss, and which produce plateaus in curves for fixation probabilities and expected times to absorption. In the FPM with n=5 role models, the population may switch between two effective equilibria, which is not possible in the IPM, or may cycle between frequencies that are not effective equilibria, which is possible in the IPM. In all observed cases of 'equilibrium switching' and 'cycling' in the FPM, model parameters exceed O(1/N), required for the diffusion approximation, resulting in an over-estimation of the actual times to absorption. However, in those cases with n=5 role models that have one effective equilibrium and stable fixation states, even if conformity coefficients exceed O(1/N), the diffusion approximation matches closely the numerical simulations of the FPM. This suggests that the robustness of the diffusion approximation depends not only on the magnitudes of coefficients, but also on the qualitative behavior of the conformity model.

Cancer cells metabolism focuses the interest of the cancer research community. Although this process is intensely studied experimentally, there are very few theoretical models that address this issue. One of the main reasons is the extraordinary complexity of the metabolism that involves numerous interdependent regulatory networks which makes the computational recreation of this complexity illusory. In this study we propose a reduced model of the metabolism which focuses on the interrelation of the three main energy metabolites which are oxygen, glucose and lactate in order to better understand the dynamics of the core system of the glycolysis-OXPHOS relationship. So simple as it is, the model highlights the main rules allowing the cell to dynamically adapt its metabolism to its changing environment. It also makes it possible to address this impact at the tissue scale. The simulations carried out in a spheroid show non-trivial spatial heterogeneity of energy metabolism. It further suggests that the metabolic features that are commonly attributed to cancer cells are not necessarily due to an intrinsic abnormality of the cells. They can emerge spontaneously due to the deregulated over-acidic environment.

We developed a mathematical model to describe healing processes in bovine corneal endothelial (BCE) cells in culture, triggered by mechanical wounds with parallel edges. Previous findings from our laboratory show that, in these cases, BCE monolayers exhibit an approximately constant healing velocity. Also, that caspase-dependent apoptosis occurs, with the fraction of apoptotic cells increasing with the distance traveled by the healing edge. In addition, in this study we report the novel findings that, for wound scratch assays performed preserving the basal extracellular matrix: i) the healing cells increase their en face surface area in a characteristic fashion, and ii) the average length of the segments of the cell columns actively participating in the healing process increases linearly with time. These latter observations preclude the utilization of standard traveling wave formalisms to model wound healing in BCE cells. Instead, we developed and studied a simple phenomenological model based on a plausible formula for the spreading dynamics of the individual healing cells, that incorporates original evidence about the process in BCE cells. The model can be simulated to: i) obtain an approximately constant healing velocity; ii) reproduce the profile of the healing cell areas, and iii) obtain approximately linear time dependences of the mean cell area and average length of the front active segments per column. In view of its accuracy to account for the experimental observations, the model can also be acceptably employed to quantify the appearance of apoptotic cells during BCE wound healing. The strategy utilized here could offer a novel formal framework to represent modifications undergone by some epithelial cell lines during wound healing.

Serology testing can identify past infection by quantifying the immune response of an infected individual providing important public health guidance. Individual immune responses are time-dependent, which is reflected in antibody measurements. Moreover, the probability of obtaining a particular measurement from a random sample changes due to changing prevalence (i.e., seroprevalence, or fraction of individuals exhibiting an immune response) of the disease in the population. Taking into account these personal and population-level effects, we develop a mathematical model that suggests a natural adaptive scheme for estimating prevalence as a function of time. We then combine the estimated prevalence with optimal decision theory to develop a time-dependent probabilistic classification scheme that minimizes the error associated with classifying a value as positive (history of infection) or negative (no such history) on a given day since the start of the pandemic. We validate this analysis by using a combination of real-world and synthetic SARS-CoV-2 data and discuss the type of longitudinal studies needed to execute this scheme in real-world settings.

Current persistent outbreak of COVID-19 is triggering a series of collective responses to avoid infection. To further clarify the impact mechanism of adaptive protection behavior and vaccination, we developed a new transmission model via a delay differential system, which parameterized the roles of adaptive behaviors and vaccination, and allowed to simulate the dynamic infection process among people. By validating the model with surveillance data during March 2020 and October 2021 in America, India, South Africa, Philippines, Brazil, UK, Spain and Germany, we quantified the protection effect of adaptive behaviors by different forms of activity function. The modeling results indicated that (1) the adaptive activity function can be used as a good indicator for fitting the intervention outcome, which exhibited short-term awareness in these countries, and it could reduce the total human infections by 3.68, 26.16, 15.23, 4.23, 7.26, 1.65, 5.51 and 7.07 times, compared with the reporting; (2) for complete prevention, the average proportions of people with immunity should be larger than 90%, 92%, 86%, 71%, 92%, 84%, 82% and 76% with adaptive protection behaviors, or 91%, 97%, 94%, 77%, 92%, 88%, 85% and 90% without protection behaviors; and (3) the required proportion of humans being vaccinated is a sub-linear decreasing function of vaccine efficiency, with small heterogeneity in different countries. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

COVID-19 remains a major public health concern, with large resurgences even where there has been widespread uptake of vaccines. Waning immunity and the emergence of new variants will shape the long-term burden and dynamics of COVID-19. We explore the transition to the endemic state, and the endemic incidence in British Columbia (BC), Canada and South Africa (SA), to compare low and high vaccination coverage settings with differing public health policies, using a combination of modelling approaches. We compare reopening (relaxation of public health measures) gradually and rapidly as well as at different vaccination levels. We examine how the eventual endemic state depends on the duration of immunity, the rate of importations, the efficacy of vaccines and the transmissibility. These depend on the evolution of the virus, which continues to undergo selection. Slower reopening leads to a lower peak level of incidence and fewer overall infections in the wave following reopening: as much as a 60% lower peak and a 10% lower total in some illustrative simulations; under realistic parameters, reopening when 70% of the population is vaccinated leads to a large resurgence in cases. The long-term endemic behaviour may stabilize as late as January 2023, with further waves of high incidence occurring depending on the transmissibility of the prevalent variant, duration of immunity, and antigenic drift. We find that long term endemic levels are not necessarily lower than current pandemic levels: in a population of 100,000 with representative parameter settings (Reproduction number 5, 1-year duration of immunity, vaccine efficacy at 80% and importations at 3 cases per 100K per day) there are over 100 daily incident cases in the model. Predicted prevalence at endemicity has increased more than twofold after the emergence and spread of Omicron. The consequent burden on health care systems depends on the severity of infection in immunized or previously infected individuals.

The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously. Each design is tested on data generated from the Lotka-Volterra model with noise added, to determine efficacy in an ideal sense. In addition to assessing each design for practical identifiability, we investigate how the predictive power of the model - i.e., its ability to fit data for initial ratios other than those to which it was calibrated - is affected by the choice of experimental design. The parallel calibration procedure is found to be optimal and is further tested on in silico data generated from a spatially-resolved cellular automaton model, which accounts for oxygen consumption and allows for variation in the intensity level of the interaction between the two cell lines. We use this study to highlight the care that must be taken when interpreting parameter estimates for the spatially-averaged Lotka-Volterra model when it is calibrated against data produced by the spatially-resolved cellular automaton model, since baseline competition for space and resources in the CA model may contribute to a discrepancy between the type of interaction used to generate the CA data and the type of interaction inferred by the LV model.

Coronavirus disease 2019 (COVID-19) booster vaccination has been implemented globally in the midst of surges in infection due to the Delta and Omicron variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The objective of the present study was to present a framework to estimate the proportion of the population that is immune to symptomatic SARS-CoV-2 infection with the Omicron variant (immune proportion) in Japan, considering the waning of immunity resulting from vaccination and naturally acquired infection. We quantified the decay rate of immunity against symptomatic infection with Omicron conferred by the second and third doses of COVID-19 vaccine. We estimated the current and future vaccination coverage for the second and third vaccine doses from February 17, 2021 to August 1, 2022 and used data on the confirmed COVID-19 incidence from February 17, 2021 to April 10, 2022. From this information, we estimated the age-specific immune proportion over the period from February 17, 2021 to August 1, 2022. Vaccine-induced immunity, conferred by the second vaccine dose in particular, was estimated to rapidly wane. There were substantial variations in the estimated immune proportion by age group because each age cohort experienced different vaccination rollout timing and speed as well as a different infection risk. Such variations collectively contributed to heterogeneous immune landscape trajectories over time and age. The resulting prediction of the proportion of the population that is immune to symptomatic SARS-CoV-2 infection could aid decision-making on when and for whom another round of booster vaccination should be considered. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Immune cells in the tumor microenvironment (TME) are known to affect tumor growth, vascularization, and extracellular matrix (ECM) deposition. Marked interest in system-scale analysis of immune species interactions within the TME has encouraged progress in modeling tumor-immune interactions in silico. Due to the computational cost of simulating these intricate interactions, models have typically been constrained to representing a limited number of immune species. To expand the capability for system-scale analysis, this study develops a three-dimensional continuum mixture model of tumor-immune interactions to simulate multiple immune species in the TME. Building upon a recent distributed computing implementation that enables efficient solution of such mixture models, major immune species including monocytes, macrophages, natural killer cells, dendritic cells, neutrophils, myeloid-derived suppressor cells (MDSC), cytotoxic, helper, regulatory T-cells, and effector and regulatory B-cells and their interactions are represented in this novel implementation. Immune species extravasate from blood vasculature, undergo chemotaxis toward regions of high chemokine concentration, and influence the TME in proportion to locally defined levels of stimulation. The immune species contribute to the production of angiogenic and tumor growth factors, promotion of myofibroblast deposition of ECM, upregulation of angiogenesis, and elimination of living and dead tumor species. The results show that this modeling approach offers the capability for quantitative insight into the modulation of tumor growth by diverse immune-tumor interactions and immune-driven TME effects. In particular, MDSC-mediated effects on tumor-associated immune species' activation levels, volume fraction, and influence on the TME are explored. Longer term, linking of the model parameters to particular patient tumor information could simulate cancer-specific immune responses and move toward a more comprehensive evaluation of immunotherapeutic strategies.

Understanding why animals organize in collective states is a central question of current research in, e.g., biology, physics, and psychology. More than 50 years ago, W.D. Hamilton postulated that the formation of animal herds may simply result from the individual's selfish motivation to minimize their predation risk. The latter is quantified by the domain of danger (DOD) which is given by the Voronoi area around each individual. In fact, simulations show that individuals aiming to reduce their DODs form compact groups similar to what is observed in many living systems. However, despite the apparent simplicity of this problem, it is not clear what motional strategy is required to find an optimal solution. Here, we use the framework of Multi Agent Reinforcement Learning (MARL) which gives the unbiased and optimal strategy of individuals to solve the selfish herd problem. We demonstrate that the motivation of individuals to reduce their predation risk naturally leads to pronounced collective behaviors including the formation of cohesive swirls. We reveal a previously unexplored rather complex intra-group motion which eventually leads to a evenly shared predation risk amongst selfish individuals.

In this work we address the problem of tumour growth control by properly exploiting a low-dimensional model that grounds on the Chemical Reaction Network (CRN) formalism. Originally conceived to work both in deterministic and stochastic frameworks, it is shown that, except for the case of very low number of tumour cells, the deterministic approach is appropriate to characterize the system behaviour, especially for control planning purposes. Two alternative control approaches are here investigated. One trivially assumes a constant infusion of external drug administration, the other is designed according to a state-feedback control scheme, with complete or partial knowledge of the state. Pros and cons of both control laws are investigated, showing that the tumour size at the beginning of the therapy plays a role of paramount importance for fixed infusion therapies, whilst only state-feedback laws can eradicate arbitrarily large tumours.