Epidemics of random walkers in metapopulation model for complete, cycle, and star graphs

Dynamics of a mistletoe-bird model on a weighted network

Based on the patchy habitats of mistletoes and the mutualistic relationship between mistletoes and birds, we propose a mistletoe-bird model on a weighted network that is described by discrete Laplacian operators. Without considering mistletoes, the dynamics of a model of birds is investigated by a threshold parameter. Under the premise of the persistence of birds, the existence and uniqueness of solutions of a mistletoe-bird model are established, and the stability of solutions of the model is discussed by the ecological reproduction index R 0 m , specifically, mistletoes go extinct whenR 0 m < 1 , and mistletoes coexist with birds whenR 0 m > 1 . Moreover, we show that network weights can induce changes of instantaneous dynamics of birds or mistletoes by the matrix perturbation method. By assuming that the weighted network is a river network and a star network, we simulate the extinction of mistletoes and the coexistence of mistletoes with birds, respectively.

Spatial dynamics of synergistic coinfection in rock-paper-scissors models

We investigate the spatial dynamics of two-disease epidemics reaching a three-species cyclic model. Regardless of their species, all individuals are susceptible to being infected with two different pathogens, which spread through person-to-person contact. We consider that the simultaneous presence of multiple infections leads to a synergistic amplification in the probability of host mortality due to complications arising from any of the co-occurring diseases. Employing stochastic simulations, we explore the ramifications of this synergistic coinfection on spatial configurations that emerge from stochastic initial conditions. Under conditions of pronounced synergistic coinfection, we identify the emergence of zones inhabited solely by hosts affected by a singular pathogen. At the boundaries of spatial domains dominated by a single disease, interfaces of coinfected hosts appear. The dynamics of these interfaces are shaped by curvature-driven processes and display a scaling behavior reflective of the topological attributes of the underlying two-dimensional space. As the lethality linked to coinfection diminishes, the evolution of the interface network's spatial dynamics is influenced by fluctuations stemming from waves of coinfection that infiltrate territories predominantly occupied by a single disease. Our analysis extends to quantifying the implications of synergistic coinfection at both the individual and population levels Our outcomes show that organisms' infection risk is maximized if the coinfection increases the death due to disease by 30% and minimized as the network dynamics reach the scaling regime, with species populations being maximum. Our conclusions may help ecologists understand the dynamics of epidemics and their impact on the stability of ecosystems.

Spatial organisation plasticity reduces disease infection risk in rock-paper-scissors models

We study a three-species cyclic game system where organisms face a contagious disease whose virulence may change by a pathogen mutation. As a responsive defence strategy, organisms' mobility is restricted to reduce disease dissemination in the system. The impact of the collective self-preservation strategy on the disease infection risk is investigated by performing stochastic simulations of the spatial version of the rock-paper-scissors game. Our outcomes show that the mobility control strategy induces plasticity in the spatial patterns with groups of organisms of the same species inhabiting spatial domains whose characteristic length scales depend on the level of dispersal restrictions. The spatial organisation plasticity allows the ecosystems to adapt to minimise the individuals' disease contamination risk if an eventual pathogen alters the disease virulence. We discover that if a pathogen mutation makes the disease more transmissible or less lethal, the organisms benefit more if the mobility is not strongly restricted, thus forming large spatial domains. Conversely, the benefits of protecting against a pathogen causing a less contagious or deadlier disease are maximised if the average size of groups of individuals of the same species is significantly limited, reducing the dimensions of groups of organisms significantly. Our findings may help biologists understand the effects of dispersal control as a conservation strategy in ecosystems affected by epidemic outbreaks.

An evolutionary game modeling to assess the effect of border enforcement measures and socio-economic cost: Export-importation epidemic dynamics

In the wake of the novel coronavirus, SARS-CoV-19, the world has undergone a critical situation in which grave threats to global public health emerged. Among human populations across the planet, travel restraints, border enforcement measures, quarantine, and isolation provisions were implemented to control and limit the spread of the contagion. Decisions on implementing and enforcing various control policies should be determined based on available real-world evidence and theoretical prediction. Further, countries around the globe-imposed force-quarantine and strict lockdown against the spreading could be unsustainable in the long run because of economic burden and people's frustration. This study proposes a novel exportation- importation epidemic model associated with behavioral dynamics under the evolutionary game theory by considering the two-body system: a source country of a contagious disease and a neighboring disease-free state. The model is first applied to the original COVID-19 data in China, Italy, and the Republic of Korea (ROK) and observed through consistent fitting results with equivalent goodness-of-fit. Then, the data are estimated per the appropriate parameters. Driven by these parametric settings and considering the normalized population, the numerical analysis, and epidemiological exploration, this work further elucidates the substantial impact of quarantine policies, healthcare facilities, socio-economic cost, and the public counter-compliance effect. Extensive numerical analysis shows that funds spent on the individual level as "emergency relief-package" can reduce the infection and improve quarantine policy success. Our results also explore that controlling border measurement can work well in the final epidemic stage of disease only if the cost is low.

Effects of pest control on a food chain in patchy environment: Species-dependent activity range on multilayer graphs

Ecosystems on earth are strongly affected by human life. We pay attention to pest control in a patchy environment. To date, many authors have reported the indeterminacy in pest control. Most of these works have been studied in single-habitat systems. In the present article, however, we consider a food chain model (prey, predator and top predator) on five networks of patches, where node and link denote habitable patch and migration path, respectively. Each network includes three layers which represent the activity ranges of respective species. Reaction-migration equations are solved analytically and numerically. It is found the dynamics largely change depending on the geometry of networks. When removal rate of top predator is increased, the so-called "top-down effect" is commonly observed. In this case, the pest control will be successful, but extinction point of top predator largely differs on different networks. When removal rate of intermediate predator is increased, the responses of system become complicated. The responses differ not only for each patch but also for each geometry. Hence, the pest control on intermediate predators may fail.

A potential game approach to modelling evolution in a connected society

When studying human behaviour, it is important to understand not just how individuals interact, but also interactions at the level of communities and populations. Most previous modelling of networks has focused on interactions between individual agents. Here we provide a modelling framework to study the evolution of behaviour in connected populations, by regarding subpopulations as the basic unit of interaction and focusing on the population-level connection structure. We find that when the underlying game played by individuals is a potential game, utilizing such a structure greatly simplifies analysis. In addition, according to known general results on the convergence of evolution dynamics to Nash equilibria in a potential game, our formulation provides a tractable model on behavioural dynamics in social networks that needs only conventional techniques from evolutionary game theory.

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

We define and study an open stochastic SIR (Susceptible-Infected-Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Population transition intensities are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock farming region in western France (Finistère) and epidemiological parameters corresponding to an infectious epizootic disease. Then we exhibit an exponential lower bound for the extinction time and the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using results inspired by the Freidlin-Wentzell theory of large deviations from a dynamical system.

Metapopulation model of rock-scissors-paper game with subpopulation-specific victory rates stabilized by heterogeneity

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.