The adaptive and innate branches of the vertebrate immune system work in close collaboration to protect organisms from harmful pathogens. As an organism ages its immune system undergoes immunosenescence, characterized by declined performance or malfunction in either immune branch, which can lead to disease and death. In this study we develop a mathematical framework of coupled innate and adaptive immune responses, namely the integrated immune branch (IIB) model. This model describes dynamics of immune components in both branches, uses a shape-space representation to encode pathogen-specific immune memory, and exhibits three steady states - health, septic death, and chronic inflammation - qualitatively similar to clinically-observed immune outcomes. In this model, the immune system (initialized in the health state) is subjected to a sequence of pathogen encounters, and we use the number of prior pathogen encounters as a proxy for the "age" of the immune system. We find that repeated pathogen encounters may trigger a fragility in which any encounter with a novel pathogen will cause the system to irreversibly switch from health to chronic inflammation. This transition is consistent with the onset of "inflammaging", a condition observed in aged individuals who experience chronic low-grade inflammation even in the absence of pathogens. The IIB model predicts that the onset of chronic inflammation strongly depends on the history of encountered pathogens; the timing of onset differs drastically when the same set of infections occurs in a different order. Lastly, the coupling between the innate and adaptive immune branches generates a trade-off between rapid pathogen clearance and a delayed onset of immunosenescence. Overall, by considering the complex feedback between immune compartments, our work suggests potential mechanisms for immunosenescence and provides a theoretical framework at the system level and on the scale of an organism's lifetime to account for clinical observations.

We present a null model to be compared with biological data to test for intrinsic persistence in movement between stops during intermittent locomotion in bounded space with different geometries and boundary conditions. We describe spatio-temporal properties of the sequence of stopping points r1,r2,r3,… visited by a Random Walker within a bounded space. The path between stopping points is not considered, only the displacement. Since there are no intrinsic correlations in the displacements between stopping points, there is no intrinsic persistence in the movement between them. Hence, this represents a null-model against which to compare empirical data for directional persistence in the movement between stopping points when there is external bias due to the bounded space. This comparison is a necessary first step in testing hypotheses about the function of the stops that punctuate intermittent locomotion in diverse organisms. We investigate the probability of forward movement, defined as a deviation of less than 90° between two successive displacement vectors, as a function of the ratio between the largest displacement between stops that could be performed by the random walker and the system size, α=Δℓ/Lmax. As expected, the probability of forward movement is 1/2 when α→0. However, when α is finite, this probability is less than 1/2 with a minimum value when α=1. For certain boundary conditions, the minimum value is between 1/3 and 1/4 in 1D while it can be even lower in 2D. The probability of forward movement in 1D is calculated exactly for all values 0<α⩽1 for several boundary conditions. Analytical calculations for the probability of forward movement are performed in 2D for circular and square bounded regions with one boundary condition. Numerical results for all values 0<α⩽1 are presented for several boundary conditions. The cases of rectangle and ellipse are also considered and an approximate model of the dependence of the forward movement probability on the aspect ratio is provided. Finally, some practical points are presented on how these results can be utilised in the empirical analysis of animal movement in two-dimensional bounded space.

Motivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic "socially distant" populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied. One of the striking features of this model is the existence of a critical implementation delay (CID) in issuing distancing mandates: while a delay of about two weeks does not have an appreciable effect on the peak number of infections, issuing mandates even slightly after this critical time results in a far greater incidence of infection. Thus, there is a nontrivial but tight "window of opportunity" for commencing social distancing in order to meet the capacity of healthcare resources. However, if one wants to also delay the timing of peak infections - so as to take advantage of potential new therapies and vaccines - action must be taken much faster than the CID. Different relaxation strategies are also simulated, with surprising results. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule's frequency. Furthermore, we considered the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines, but the negative effects can be mitigated if the relaxation strategy is carefully designed.

Metacommunity membership is influenced by habitat availability and trophic requirements. However, for multitrophic horizontally transmitted symbiont communities that are closely associated with hosts, symbiont-host interactions may affect membership criteria in novel ways. For example, failure of beneficial services from symbionts could influence the host, and in turn, the entire community. Understanding such host-symbiont feedback effects on symbiont community membership, symbiont community structure, and function is important for understanding if host-symbiont communities are fundamentally different from more traditional ecological communities. We investigate the membership criteria for a multitrophic insect symbiont community that colonizes host inflorescences at specific developmental stages termed colonization windows. The inflorescences serve as microcosm habitats. Symbionts exhibit a range of interactions from mutualism to parasitism. Hosts exhibit feedback by aborting inflorescences not pollinated by mutualistic symbionts. Habitats are consequently lost for all other symbiont species in such host-derived organs whose development is mutualist-dependent. Using empirical measurements to characterize inflorescence development, we simulate symbiont dispersal colonization across hosts. We vary host densities and lengths of symbiont colonization windows, and track the persistence of each symbiont species in the metacommunity based on its trophic requirements and resource availability within the microcosm. Since the persistence of the microcosm habitat is dictated by pollination performed by the mutualist, the mutualist fared better than all other symbionts. The length of symbiont colonization windows was positively related with colonization success and symbiont persistence. The cumulative length of the colonization windows of prey dictated predator success; diet breadth or prey colonization success did not influence predator persistence. Predators also had a greater host-plant density requirement than prey for persistence in the community. These results offer valuable insights into host densities required for maintaining symbionts, and have implications for multitrophic symbiont community stability. Special constraints can govern symbiont community membership, function and structure and symbiont persistence when host-symbiont feedback impacts host microcosm development.

In many terrestrial, marine, and freshwater predator-prey communities, young predators can be vulnerable to attacks by large prey. Frequent prey counter-attacks may hinder the persistence of predators. Despite the commonness of such role reversals in nature, they have rarely been addressed in evolutionary modelling. To understand how role reversals affect ecological and evolutionary dynamics of a predator-prey community, we derived an ecological model from individual-level processes using ordinary differential equations. The model reveals complex ecological dynamics, with possible bistability between alternative coexistence states and an Allee effect for the predators. We find that when prey counter-attacks are frequent, cannibalism is necessary for predator persistence. Using numerical analysis, we also find that a sudden ecological shift from coexistence to predator extinction can occur through several catastrophic bifurcations, including 'saddle-node', 'homoclinic', and 'subcritical Hopf'. The analysis of single-species evolution reveals that predator selection towards increasing or decreasing cannibalism triggers a catastrophic shift towards an extinction state of the predators. Such an evolutionary extinction of the predators may also be caused by prey selection towards increasing foraging activity because it facilitates encounters with vulnerable, young predators. The analysis of predator-prey coevolution further demonstrates that predator's catastrophic extinction becomes an even more likely outcome than in single-species evolution. Our results suggest that when young predators are vulnerable to prey attacks, a sudden extinction of the predators may be more common than currently understood.

Legumes produce root nodules containing symbiotic rhizobial bacteria that convert atmospheric molecular nitrogen into ammonia or related nitrogenous compounds. The host plant supplies photosynthetic products to root nodules forming a mutualistic system. Legumes have physiological mechanisms for regulating nodule production with chemical signals produced in leaves, called the autoregulation of nodulation. In this paper, we discuss the optimal number of root nodules that maximizes the performance of the host plant. Here, we study two models. In the stationary plant model, the acquired photosynthetic products minus cost and loss are used for reproduction. In the growing plant model, the excess material is invested to produce leaves, roots, and root nodules, resulting in the exponential growth of the whole plant. The analysis shows that having root nodules is beneficial to the plant for a high leaf nitrogen content, faster plant growth rate, a short leaf longevity, a low root/shoot ratio, and low soil nutrient concentration. We discuss the long-distance control of nodulation-autoregulation and dependence on the environmental conditions of terrestrial plants considering these results.

We consider a Prisoner's Dilemma (PD) that is repeated with some probability 1-ρ only between cooperators as a result of an opting-out strategy adopted by all individuals. The population is made of N pairs of individuals and is updated at every time step by a birth-death event according to a Moran model. Assuming an intensity of selection of order 1/N and taking 2N2 birth-death events as unit of time, a diffusion approximation exhibiting two time scales, a fast one for pair frequencies and a slow one for cooperation (C) and defection (D) frequencies, is ascertained in the limit of a large population size. This diffusion approximation is applied to an additive PD game, cooperation by an individual incurring a cost c to the individual but providing a benefit b to the opponent. This is used to obtain the probability of ultimate fixation of C introduced as a single mutant in an all D population under selection, which can be compared to the probability under neutrality, 1/(2N), as well as the corresponding probability for a single D introduced in an all C population under selection. This gives conditions for cooperation to be favored by selection. We show that these conditions are satisfied when the benefit-to-cost ratio, b/c, exceeds some increasing function of ρ that is approximately given by (1+ρ)/(1-ρ). This condition is more stringent, however, than the condition for tit-for-tat (TFT) to be favored against always-defect (AllD) in the absence of opting-out.

Proboscises of many fluid-feeding insects share a common architecture: they have a partially open food canal along their length. This feature has never been discussed in relation to the feeding mechanism. We formulated and solved a fluid mechanics model of fluid uptake and estimated the time required to completely fill the food canal of the entire proboscis through the openings along its length. Butterflies and moths are taken as illustrative and representative of fluid-feeding insects. We demonstrated that the proposed mechanism of filling the proboscis with fluid through permeable lengthwise bands, in association with a thin film of saliva in the food canal, offers a competitive pathway for fluid uptake. Compared with the conventional mechanism of fluid uptake through apically restricted openings, the new mechanism provides a faster rate of fluid uptake, especially for long-tongued insects. Accordingly, long-tongued insects with permeable lengthwise bands would be able to more rapidly exploit a broader range of liquids in the form of films, pools, and discontinuous columns, thereby conserving energy and minimizing exposure to predators, particularly for hovering insects.

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.

Given maximal social distancing duration and intensity, how can one minimize the epidemic final size, or equivalently the total number of individuals infected during the outbreak? A complete answer to this question is provided and demonstrated here for the SIR epidemic model. In this simplified setting, the optimal solution consists in enforcing the highest confinement level during the longest allowed period, beginning at a time instant that is the unique solution to certain 1D optimization problem. Based on this result, we present numerical essays showing the best possible performance for a large set of basic reproduction numbers and lockdown durations and intensities.

BACKGROUND: Seroepidemiological surveillance data has been demonstrated to be useful for estimating the cumulative incidence of influenza, and measures the difference between pre- and post-epidemic seropositive fractions. Despite this, such studies relied on a chosen cut-off value for seropositivity. The aim of the present study is to develop a method to analyze distributions of serial cross-sectional seroepidemiological surveillance datasets using an epidemiological model so that the transmission potential can be estimated without imposing a cut-off value. METHODS: A mathematical model of influenza transmission with a discrete antibody titer level was constructed. The final size equation for pre- and post-epidemic titer levels was derived. Subsequently, using the estimated distribution of the dilution increase caused by infection and the measurement error distribution, the model parameters were optimized using the maximum likelihood method. A bootstrap-based confidence interval calculation and sensitivity analysis were also performed. RESULTS: Without imposing a cut-off value, the cumulative incidence was quantified, thereby yielding an estimate of the basic reproduction number. For the purpose of exposition, the proposed method was applied to influenza A/Victoria/3/75(H3N2) data, and serological data between 1975 and 1976 were compared. The estimated reproduction number was greater than that using the cut-off value of the hemagglutination inhibition level with titer level 20 (dilution 1:20) or above to define positives. CONCLUSION: The proposed method without a cut-off value offers an unbiased approach to estimating the cumulative incidence along with the reproduction number. If a cut-off value is required, the results imply that titer level 20 or above may better represent a reasonable cut-off value for calculating the incidence, but it could underestimate the basic reproduction number.

Variation is characteristic of all living systems. Laboratory techniques such as flow cytometry can probe individual cells, and, after decades of experimentation, it is clear that even members of genetically identical cell populations can exhibit differences. To understand whether variation is biologically meaningful, it is essential to discern its source. Mathematical models of biological systems are tools that can be used to investigate causes of cell-to-cell variation. From mathematical analysis and simulation of these models, biological hypotheses can be posed and investigated, then parameter inference can determine which of these is compatible with experimental data. Data from laboratory experiments often consist of "snapshots" representing distributions of cellular properties at different points in time, rather than individual cell trajectories. These data are not straightforward to fit using hierarchical Bayesian methods, which require the number of cell population clusters to be chosen a priori. Nor are they amenable to standard nonlinear mixed effect methods, since a single observation per cell is typically too few to estimate parameter variability. Here, we introduce a computational sampling method named "Contour Monte Carlo" (CMC) for estimating mathematical model parameters from snapshot distributions, which is straightforward to implement and does not require that cells be assigned to predefined categories. The CMC algorithm fits to snapshot probability distributions rather than raw data, which means its computational burden does not, like existing approaches, increase with the number of cells observed. Our method is appropriate for underdetermined systems, where there are fewer distinct types of observations than parameters to be determined, and where observed variation is mostly due to variability in cellular processes rather than experimental measurement error. This may be the case for many systems due to continued improvements in resolution of laboratory techniques. In this paper, we apply our method to quantify cellular variation for three biological systems of interest and provide Julia code enabling others to use this method.

A general stochastic model for susceptible → infective → recovered (SIR) epidemics in non-homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex models. The basic reproduction number R0, an indication of the probability of an outbreak for homogeneous populations does not indicate the probability of an outbreak for non-homogeneous models anymore, because it changes with the initially infected case. Therefore, we use "individual R0" that is the expected number of secondary cases for a unique given initially infected individual. Thus, the effectiveness of intervention strategies can be assessed by their capability to reduce individual R0 values. Also a vaccination plan based on individual R0 values for fully heterogeneous populations is proposed. It is based on the recursive calculation of individual R0 values.

DNA molecules containing repetitive motifs are prone to expand in their lengths. Once there appear a head to tail tandem of two identical DNA sequences in the system, they can propagate indefinitely by the mechanism involving cycles of staggered annealing of complementary DNA strands of variable lengths and polymerase mediated filling-in of the generated overhangs. Microgene Polymerization Reaction (MPR) is an experimental model for expansion of short repetitive DNA to longer lengths. The testable kinetic model of (MPR) was formulated and solved numerically by Itsko et al. in Kinetics of Repeat Propagation in the Microgene Polymerization Reaction (2009). Here, the simple cases of MPR were solved analytically using modified Smoluchowski coagulation equation. It was found that the repeats propagate according to Gumbel probability density function when the distribution of lengths of obtained polymers follows inverted Gumbel probability density function.

Etosha National Park (ENP) is located in Namibia, where an annual anthrax outbreak (caused by Bacillus anthracis) occurs among grazing animals such as zebras. This increases the number of carcasses in ENP, allowing for scavengers such as jackals to feed off these carcasses. Carcasses provide a location of conspecific interaction between jackals and may be a means of disease transmission among the jackals. We are interested in studying how a disease in the zebra population may help to propagate a different disease (rabies) in the jackal population since the carcasses are providing a location of interaction between the jackals. We aim to answer the following research question: how do anthrax and rabies affect each other's ability to spread? Standard qualitative analysis techniques distinguished outcomes (stable equilibria) using reproduction numbers as threshold quantities. We found that rabies helps anthrax, and a little anthrax helps rabies invade, but a lot of anthrax prevents rabies by reducing the jackal population through its food source.