Complex interactions are at the root of the population dynamics of many natural systems, particularly for being responsible for the allocation of species and individuals across apposite niches of the ecological landscapes. On the other side, the randomness that unavoidably characterises complex systems has increasingly challenged the niche paradigm providing alternative neutral theoretical models. We introduce a network-inspired metapopulation individual-based model (IBM), hereby named self-segregation, where the density of individuals in the hosting patches (local habitats) drives the individuals spatial assembling while still constrained by nodes' saturation. In particular, we prove that the core-periphery structure of the networked landscape triggers the spontaneous emergence of vacant habitat patches, which segregate the population in multistable patterns of isolated (sub)communities separated by empty patches. Furthermore, a quantisation effect in the number of vacant patches is observed once the total system mass varies continuously, emphasising thus a striking feature of the robustness of population stationary distributions. Notably, our model reproduces the patch vacancy found in the fragmented habitat of the Glanville fritillary butterfly Melitaea cinxia, an endemic species of the Åland islands. We argue that such spontaneous breaking of the natural habitat supports the concept of the highly contentious (Grinnellian) niche vacancy and also suggests a new mechanism for the endogeneous habitat fragmentation and consequently the peripatric speciation.

Plant-microbe symbiosis is pervasive in the Earth's ecosystems and dates back to the early land colonisation by plants. Mutualistic partnership with rhizobia bacteria and mycorrhizal fungi promotes plant nutrition, growth and diversity, impacting important ecosystem functions. However, how the global behaviour and dynamical properties of an ecosystem are modified by plant-microbe symbiosis is still unclear. To tackle this theoretical question, we resorted to the Daisyworld as a toy model of the global ecosystem. We redesigned the original model to allow accounting for seed production, spreading, germination, and seedling development to mature seed-producing plants to describe how symbiotic and non-symbiotic daisy species differ in these key processes. Using the steady-state and bifurcation analysis of this model, we demonstrate that symbiosis with microbes broadens the habitability range of the Daisyworld by enhancing plant growth and/or facilitating plant access to otherwise uninhabitable nutrient-poor regions.

Shanghai suffered a large outbreak of Omicron mutant of COVID-19 at the beginning of March 2022. To figure out the spatiotemporal patterns of the epidemic, a retrospective statistical investigation, coupled with a dynamic model, is implemented in this study. The hotspots of SARS-CoV-2 transmissions are identified, and strong aggregative effects in the decay stage are found. Besides, the visualization of disease diffusion is provided to show how COVID-19 disease invades all districts of Shanghai in the early stage. Furthermore, the calculations from the dynamic model manifest the effect of detections to suppress the epidemic dissemination. These results reveal the strategies to improve the spatial control of disease.

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system's potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

Since the mid-1990s, growing concerns over antimicrobial resistant (AMR) organisms has led to an increase in the use of mathematical models to explore the inter-host transmission of such infections. Previous work reviewing such models categorised them into generic frameworks based on their underlying assumptions. These assumptions dictated the coexistence between AMR and antimicrobial sensitive strains. We add to this work performing stability analyses of the frameworks, along with simulating them deterministically and stochastically. Stability analyses found that many of these assumptions lead to models having the same equilibria, but showed differences in the equilibria's stability between models. Deterministic simulations reveal that assuming replacement of one infecting strain by another leads to an unusual antimicrobial treatment threshold. Increasing beyond this threshold causes a discontinuous increase in disease burden. The cost of AMR to pathogen fitness (lowered transmission) dictates both the threshold of treatment that causes the discontinuous increase in disease burden and the size of that increase. It was also shown that Superinfection states can be biased against resident strains and so favour coexistence of both strains. Stochastic simulations demonstrated that differing scenario starting conditions can guide models to converge upon equilibria that they may not have under deterministic simulation. These findings highlight the importance of checking assumptions when modelling AMR and strain competition more widely.

MicroRNAs (miRs) regulatory network models are highly non-linear due to the negative regulation of gene expression at the post-transcriptional level by miRs and can produce interesting dynamics of the system such as bistability for miR-transcriptional factors interactions. In this article, we focus on the miR-17-92 cluster and its interaction with transcriptional factors (proteins) E2F and Myc. Environmental fluctuations (noise) and randomness in the bio-chemical reactions can be very important and change the dynamical role of miR-17-92 in the regulatory network. We have formulated a stochastically forced miR-17-92 and E2F-Myc interaction model and study the phenomena of intrinsic and extrinsic noise which can induce random switching between steady states or the destruction of the bistability. Using a method that employs stochastic sensitivity functions we have constructed confidence ellipses to determine the configurational arrangements of equilibrium and spatial arrangements of random states near stable equilibria. Simulations are carried out to numerically show the flow of the solution trajectories under noise. Finally, we summarize the simulation results and the impact of noise on the dual non-linear role of miR-17-92 cluster to act as an oncogene or as a tumour suppressor gene.

Given an endemic infectious disease and a budget, how do we optimally allocate interventions to control the disease? This paper shows that the optimal strategy varies depending on the budget, the type of intervention, the trajectory of pathogen load, and the objective. Using a model with explicit within- and between-host dynamics, we model isolation, supportive treatment, and specific treatment. Isolation and supportive treatment affect the transmission coefficient and the disease-induced mortality rate, respectively, in the between-host dynamics. Specific treatment affects the clearance rate of pathogens in the within-host dynamics. We study the optimisation of the three interventions for various budget levels via evaluating isolation and supportive treatment at the population level and specific treatment at both the population and individual levels. At the population level, we consider the risk of transmission, the burden of illness, and the survival probability, and to that end, we choose the population-level infection rate, the population density of infected individuals, and the total disease-induced mortality rate as objective functions. At the individual level, we consider the length of infection and the pathogen load, and to that end, we choose the maximum infection-age and the maximum pathogen load as objective functions. The objective is to minimise these functions through varying two variables that refer to when the intervention starts and when it stops for an infected individual and also indicate what kind of individuals can get the intervention from the population perspective. We find that the optimal strategy of isolation is to isolate individuals with a higher pathogen load, given a lower budget. The optimal strategy of supportive treatment can be the same as isolation or simply no treatment. The optimal strategy of specific treatment is complicated, and it can be to treat individuals with pathogen loads above a particular level until they recover or until the pathogens can decrease when treatment stops, or it can be another scenario.

Understanding and predicting critical transitions in spatially explicit ecological systems is particularly challenging due to their complex spatial and temporal dynamics and high dimensionality. Here, we explore changes in population distribution patterns during a critical transition (an extinction event) using computational topology. Computational topology allows us to quantify certain features of a population distribution pattern, such as the level of fragmentation. We create population distribution patterns via a simple coupled patch model with Ricker map growth and nearest neighbors dispersal on a two dimensional lattice. We observe two dominant paths to extinction within the explored parameter space that depend critically on the dispersal rate d and the rate of parameter drift, Δϵ. These paths to extinction are easily topologically distinguishable, so categorization can be automated. We use this population model as a theoretical proof-of-concept for the methodology, and argue that computational topology is a powerful tool for analyzing dynamical changes in systems with noisy data that are coarsely resolved in space and/or time. In addition, computational topology can provide early warning signals for chaotic dynamical systems where traditional statistical early warning signals would fail. For these reasons, we envision this work as a helpful addition to the critical transitions prediction toolbox.

The concept of doubling time has been increasingly used since the onset of the coronavirus disease 2019 (COVID-19) pandemic, but its characteristics are not well understood, especially as applied to infectious disease epidemiology. The present study aims to be a practical guide to monitoring the doubling time of infectious diseases. Via simulation exercise, we clarify the epidemiological characteristics of doubling time, allowing possible interpretations. We show that the commonly believed relationship between the doubling time and intrinsic growth rate in population ecology does not strictly apply to infectious diseases, and derive the correct relationship between the two. We examined the impact of varying (i) the growth rate, (ii) the starting point of counting cumulative number of cases, and (iii) the length of observation on statistical estimation of doubling time. It was difficult to recover values of growth rate from doubling time, especially when the growth rate was small. Starting time period is critical when the statistical estimation of doubling time occurs during the course of an epidemic. The length of observation was critical in determining the overall magnitude of doubling time, and when only the latest 1-2 weeks' data were used, the resulting doubling time was very short, regardless of the intrinsic growth rate r. We suggest that doubling time estimates of infectious disease epidemics should at a minimum be accompanied by descriptions of (i) the starting time at which the cumulative count is initiated and (ii) the length of observation.

People are more likely to interact with other people of their ethnicity-a phenomenon known as ethnic homophily. In the United States, people of color are known to hold proportionately more high-contact jobs and are thus more at risk of virus infection. At the same time, these ethnic groups are on average younger than the rest of the population. This gives rise to interesting disease dynamics and non-trivial trade-offs that should be taken into consideration when developing prioritization strategies for future mass vaccine roll-outs. Here, we study the spread of COVID-19 through the US population, stratified by age, ethnicity, and occupation, using a detailed, previously-developed compartmental disease model. Based on historic data from the US mass COVID-19 vaccine roll-out that began in December 2020, we show, (i) how ethnic homophily affects the choice of optimal vaccine allocation strategy, (ii) that, notwithstanding potential ethical concerns, differentiating by ethnicity in these strategies can improve outcomes (e.g., fewer deaths), and (iii) that the most likely social context in the United States is very different from the standard assumptions made by models which do not account for ethnicity and this difference affects which allocation strategy is optimal. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The introduction of noise to signals can alter central regulatory switches of cellular processes leading to diseases. Noise is inherently present in the cellular signalling system and plays a decisive role in the input-output (I/O) relation. The current study aims to understand the noise tolerance of motif structures in the cell signalling processes. The vulnerability of a node to noise could be a significant factor in causing signalling error and need to be controlled. We developed stochastic differential equation (SDE) based mathematical models for different network motifs with two nodes and studied the association between motif structure and signal-noise relation. A two-dimensional parameter space analysis on motif sensitivity with noise and input signal variation was performed to classify and rank the motifs. Identifying sensitive motifs and their high druggability infers their significance in screening potential drug-target candidates. Finally, we proposed a theoretical framework to identify nodes from a network as potential drug targets. We applied this mathematical formalism to three cancer networks to identify drug-targets and validated them with existing databases.

Hair follicles (HFs) are stem-cell-rich mammalian mini-organs that can undergo cyclic regenerations over the life span of the organism. The cycle of a HF consists of three consecutive phases: anagen-the active proliferation phase, catagen-the degeneration phase, and telogen-the resting phase. While HFs undergo irreversible degeneration during catagen, recent experimental research on mice shows that when anagen HFs are subject to ionizing radiation (IR), they undergo a transient degeneration, followed by a nearly full regeneration that makes the HFs return to homeostatic state. The mechanisms underlying these IR-induced HF regenerative dynamics and the catagen degenerative dynamics, remain unknown. In this work, we develop an ODE type cell differentiation population model to study the control mechanisms of HF regeneration. The model is built based on current theoretical knowledge in biology and mathematically formulated using feedback mechanisms. Model parameters are calibrated to IR experimental data, and we then provide modeling results with both deterministic ODE simulations and corresponding stochastic simulations. We perform stability and bifurcation analyses on the ODE model, which reveal that for anagen HFs, a low spontaneous apoptosis rate secures the stability of the HF homeostatic steady state, allowing the HF to regenerate even when subject to strong IR. On the other hand, the irreversible degeneration during catagen results from both strong spontaneous apoptosis rate and strong apoptosis feedback. Lastly, we perform sensitivity analysis to identify key parameters in the model to validate these hypotheses.

Cells process environmental cues by activating intracellular signaling pathways with numerous interconnections and opportunities for cross-regulation. We employed a systems biology approach to investigate intersections of kinase p38, a context-dependent tumor suppressor or promoter, with Akt and ERK, two kinases known to promote cell survival, proliferation, and drug resistance in cancer. Using live, single cell microscopy, multiplexed fluorescent reporters of p38, Akt, and ERK activities, and a custom automated image-processing pipeline, we detected marked heterogeneity of signaling outputs in breast cancer cells stimulated with chemokine CXCL12 or epidermal growth factor (EGF). Basal activity of p38 correlated inversely with amplitude of Akt and ERK activation in response to either ligand. Remarkably, small molecule inhibitors of p38 immediately decreased basal activities of Akt and ERK but increased the proportion of cells with high amplitude ligand-induced activation of Akt signaling. To identify mechanisms underlying cross-talk of p38 with Akt signaling, we developed a computational model incorporating subcellular compartmentalization of signaling molecules by scaffold proteins. Dynamics of this model revealed that subcellular scaffolding of Akt accounted for observed regulation by p38. The model also predicted that differences in the amount of scaffold protein in a subcellular compartment captured the observed single cell heterogeneity in signaling. Finally, our model predicted that reduction in kinase signaling can be accomplished by both scaffolding and direct kinase inhibition. However, scaffolding inhibition can potentiate future kinase activity by redistribution of pathway components, potentially amplifying oncogenic signaling. These studies reveal how computational modeling can decipher mechanisms of cross-talk between the p38 and Akt signaling pathways and point to scaffold proteins as central regulators of signaling dynamics and amplitude.

This paper formalizes selection on a quantitative trait affecting the evolution of behavior (or development) rules through which individuals act and react with their surroundings. Combining Hamilton's marginal rule for selection on scalar traits and concepts from optimal control theory, a necessary first-order condition for the evolutionary stability of the trait in a group-structured population is derived. The model, which is of intermediate level of complexity, fills a gap between the formalization of selection on evolving traits that are directly conceived as actions (no phenotypic plasticity) and selection on evolving traits that are conceived as strategies or function valued actions (complete phenotypic plasticity). By conceptualizing individuals as open deterministic dynamical systems expressing incomplete phenotypic plasticity, the model captures selection on a large class of phenotypic expression mechanisms, including developmental pathways and learning under life-history trade-offs. As an illustration of the results, a first-order condition for the evolutionary stability of behavior response rules from the social evolution literature is re-derived, strengthened, and generalized. All results of the paper also generalize directly to selection on multidimensional quantitative traits affecting behavior rule evolution, thereby covering neural and gene network evolution.

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

The mosquito-borne disease, malaria, continues to impose a devastating health and economic burden worldwide. In malaria-endemic areas, insecticide-treated nets (ITNs) have been useful in curtailing the burden of the disease. However, mosquito resistance to insecticides, decay in ITN efficacy, net attrition, etc., undermine the effectiveness of ITNs in combatting malaria. In this study, mathematical models that account for asymptomatic infectious humans (through a partially immune class or a separate asymptomatic infectious class), insecticide resistance, and decay in ITN efficacy are proposed and analyzed. Analytical and numerical results of the models when ITN efficacy is constant show that there are parameter regimes for which a backward bifurcation occurs. Local and global sensitivity analyses are performed to identify parameters (some of which are potential targets for disease control) with the most significant influence on the control reproduction (Rc) and disease prevalence. These influential parameters include the maximum biting rate of resistant mosquitoes, ITN coverage, initial ITN efficacy against sensitive mosquitoes, the probability that an infectious mosquito (human) infects a susceptible human (mosquito), and the rate at which adult mosquitoes develop (lose) resistance to insecticides. Simulations of the models show that accounting for asymptomatic infectious humans through a separate class, or not accounting for the decay in ITN efficacy leads to an underestimation of disease burden. In particular, if the initial efficacy of ITNs against sensitive and resistance mosquitoes is 96%, the minimum ITN coverage required to reduce Rc below one (and hence, contain malaria) is approximately 11% (27%) lower when ITN efficacy is averaged (constant) for a model with a separate asymptomatic class. For the model with a partially immune class and decaying ITN efficacy, reducing Rc below one is impossible even if the entire populace uses ITNs. The study shows that replacing ITNs before their prescribed lifespans, or designing ITNs with longer lifespans is important for malaria control. Furthermore, the study shows that piperonyl butoxide (PBO) ITNs (which inhibit or reverse insecticide resistance) outperform regular ITNs in malaria control. Hence, prospects for effectively controlling malaria are enhanced by widespread use of high quality ITNs (e.g. PBO ITNs), especially if the useful lifespans of the ITNs are long enough and the ITNs are replaced before the end of their useful lifespans.

Seasonal influenza causes vast public health and economic impact globally. The prevention and control of the annual epidemics remain a challenge due to the antigenic evolution of the viruses. Here, we presented a novel modeling framework based on changes in amino acid sequences and relevant epidemiological data to retrospectively investigate the competitive evolution and transmission of H1N1 and H3N2 influenza viruses in the United States during October 2002 and April 2019. To do so, we estimated the time-varying disease transmission rate from the reported influenza cases and the time-varying antigenic change rate of the viruses from the changes in amino acid sequences. By incorporating the time-varying antigenic change rate into the transmission models, we found that the models could capture the evolutionary transmission dynamics of influenza viruses in the United States. Our modeling results also showed that the antigenic change of the virus plays an essential role in seasonal influenza dynamics.

We develop a lattice-based, hybrid discrete-continuum modeling framework for SARS-CoV-2 exposure and infection in the human lung alveolar region, or parenchyma, the massive surface area for gas exchange. COVID-19 pneumonia is alveolar infection by the SARS-CoV-2 virus significant enough to compromise gas exchange. The modeling framework orchestrates the onset and progression of alveolar infection, spatially and temporally, beginning with a pre-immunity baseline, upon which we superimpose multiple mechanisms of immune protection conveyed by interferons and antibodies. The modeling framework is tunable to individual profiles, focusing here on degrees of innate immunity, and to the evolving infection-replication properties of SARS-CoV-2 variant strains. The model employs partial differential equations for virion, interferon, and antibody concentrations governed by diffusion in the thin fluid coating of alveolar cells, species and lattice interactions corresponding to sources and sinks for each species, and multiple immune protections signaled by interferons. The spatial domain is a two-dimensional, rectangular lattice of alveolar type I (non-infectable) and type II (infectable) cells with a stochastic, species-concentration-governed, switching dynamics of type II lattice sites from healthy to infected. Once infected, type II cells evolve through three phases: an eclipse phase during which RNA copies (virions) are assembled; a shedding phase during which virions and interferons are released; and then cell death. Model simulations yield the dynamic spread of, and immune protection against, alveolar infection and viral load from initial sites of exposure. We focus in this paper on model illustrations of the diversity of outcomes possible from alveolar infection, first absent of immune protection, and then with varying degrees of four known mechanisms of interferon-induced innate immune protection. We defer model illustrations of antibody protection to future studies. Results presented reinforce previous recognition that interferons produced solely by infected cells are insufficient to maintain a high efficacy level of immune protection, compelling additional mechanisms to clear alveolar infection, such as interferon production by immune cells and adaptive immunity (e.g., T cells). This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".