Superinfection Behaviors on Scale-Free Networks with Competing Strains

This paper considers the epidemiology of two strains (I,J) of a disease spreading through a population represented by a scale-free network. The epidemiological model is SIS and the two strains have different reproductive numbers. Superinfection means that strain I can infect individuals already infected with strain J, replacing the strain J infection. Individuals infected with strain I cannot be infected with strain J. The model is set up as a system of ordering differential equations and stability of the disease free, marginal strain I and strain J, and coexistence equilibria are assessed using linear stability analysis, supported by simulations. The main conclusion is that superinfection, as modeled in this paper, can allow strain I to coexist with strain J even when it has a lower basic reproductive number. Most strikingly, it can allow strain I to persist even when its reproductive number is less than 1.     

The evolutionary dynamics of a spatial multi-strain host-pathogen system with cross-immunity

We considered a Susceptible-Infective-Recovered-Susceptible (SIRS) model with strain mutation and cross-immunity in a non-spatial model and a lattice-structured model, where all individuals can reproduce if the space/resources allow. In the lattice-structured model, both the host reproduction and pathogen transmission processes are assumed to interact with next nearest neighbors, and the model was analyzed by an improved pair approximation (IPA). A family of correlated equations of pair approximation and mean-field were presented. We show the phase diagram of the coexistence and extinction which were obtained from parameterization by measuring the basic reproduction numbers of the strains during their infection processes. The qualitative results of the pair approximation model are similar to that of the corresponding non-spatial model. Furthermore, the spatial model predicts coexistence over a wider range of parameters than the non-spatial model. In particular, when the strain evolution tends to a larger basic reproduction number, the correlated spatial approximation could predict better than the mean-field approximation.     

SIS reaction–diffusion model with risk-induced dispersal under free boundary

A spatial susceptible–infected–susceptible epidemic model with a free boundary, where infected individuals disperse non-uniformly, is investigated in this study. Spatial heterogeneity and movement of individuals are essential factors that affect pandemics and the eradication of infectious diseases. Our goal is to investigate the effect of a dispersal strategy for infected individuals, known as risk-induced dispersal (RID), which represents the motility of infected individuals induced by risk depending on whether they are in a high- or a low-risk region. We first construct the basic reproduction number and then understand the manner in which a nonuniform movement of infected individuals affects the spreading–vanishing dichotomy of a disease in a one-dimensional domain. We conclude that even though the infected individuals reside in a high-risk initial domain, the disease can be eradicated from the region if the infected individuals move with a high sensitivity of RID as they disperse. Finally, we demonstrate our results via simulations for a one-dimensional case.     

具Ⅱ型Holling功能性反应强耦合椭圆系统的共存问题

本文研究带齐次Dirichlet边界条件的强耦合椭圆系统,首先证明了当食饵和捕食者的扩散率足够大,或者出生率足够小时,系统不存在共存现象,并给出半平凡解存在的充分条件．然后利用Schauder不动点定理,得到强耦合的椭圆问题至少有一个正解存在的充分条件．该条件说明只要捕食者的内部竞争强,物种的交叉扩散相对弱,或者捕获率足够小,物种的交叉扩散相对弱,强耦合系统就至少有一个正解存在．     

Effect of emergent carrying capacity in an eco‐epidemiological system

The paper explores an eco‐epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S‐I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non‐infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco‐epidemiological models. We observed that different intra‐class and inter‐class competition can facilitate the coexistence of susceptible prey‐infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi‐stability. The present system undergoes bi‐stability in two different scenarios: (a) bi‐stability between the planner equilibria where susceptible prey co‐exists with predator or infected prey and (b) bi‐stability between co‐existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease‐free equilibrium are worked out. Copyright © 2015 John Wiley & Sons, Ltd.     

On a strain-structured epidemic model

We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the interesting scenario when individuals infected with different strains cause secondary (new) infections at different rates. Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption. Our main motivation is to study competition between different strains of a virus/bacteria. From the mathematical point of view, we are interested whether the nonlinear infection process leads to a well-posed model. We use a semilinear formulation to show global existence and positivity of solutions up to a critical value of the exponent in the nonlinearity. Furthermore, we establish the existence of the endemic steady state for particular classes of nonlinearities.     

Arrow's Theorem,Weglorz' Models and the Axiom of Choice

Applying Weglorz' mode s of set theory without the axiom of choice, we investigate Arrow‐type social we fare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying “finite discrimination”, if and only if in Weglorz' mode there is a free ultrafilter on a set representing the individuals.     

Global dynamics of a predator–prey model with time delay and stage structure for the prey

A stage-structured predator–prey system with Holling type-II functional response and time delay due to the gestation of predator is investigated. By analyzing the characteristic equations, the local stability of each of feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when both the predator-extinction equilibrium and the coexistence equilibrium are not feasible, and that the predator-extinction equilibrium is globally asymptotically stable if the coexistence equilibrium does not exist, and sufficient conditions are derived for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results.     

带有脉冲免疫和传染年龄的传染病模型的全局吸引性

讨论了带有脉冲免疫和传染年龄的传染病模型.传染类的恢复率是传染年龄的函数,当染病再生数小于1时,文章得到无病周期解是全局吸引的.如果总人口规模变化,也可得到类似的结论.最后,提出了带有脉冲免疫和传染年龄传染病模型待解决的问题.     

Probability of a major infection in a stochastic within-host model with multiple stages

Establishment or spread of a viral infection within healthy individuals depends on exposure to a viral source, either through virus particles or through cells that have been infected. We assume that a potential infection has reached the site of the healthy target cells and we apply stochastic within-host models and multitype branching processes to investigate whether a major infection becomes established. The model includes multiple latent and actively infected stages. It is shown that the probability of a major infection is generally more likely after the virus has entered the target cell and the cell is actively infected. In some cases, the probability of a major infection is less likely if the burst size of actively infected cells is small.     

A Leslie-Gower Holling-type II ecoepidemic model

The modified Leslie-Gower and Holling-type II predator-prey model is generalized in the context of ecoepidemiology, with disease spreading only among the prey species. A new feature is introduced, the intraspecific competition of infected prey. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibrium is shown.     

一类具交错扩散的互惠模型的共存解

研究了Dirichlet边界条件下具交错扩散的两种群互惠模型.采用上下解方法,结合Schauder不动点理论,给出了问题共存解存在的充分条件.进一步,利用单调迭代序列的方法构造出问题的共存解.结果表明,当交错扩散相对弱时,问题至少存在一共存解.     

Avian-human influenza epidemic model with diffusion

A diffusive epidemic model is investigated. This model describes the transmission of avian influenza among birds and humans. The behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by spectral analysis and by using Lyapunov functional. Our result shows that the disease-free equilibrium is globally asymptotically stable, if the contact rate for the susceptible birds and the contact rate for the susceptible humans are small. It suggests that the best policy to prevent the occurrence of a pandemic is not only to exterminate the infected birds with avian influenza but also to reduce the contact rate for susceptible humans with the individuals infected with mutant avian influenza. Numerical simulations are presented to illustrate the main results.     

一类多菌株STD模型的共存性

我们已经研究过一类拥有两种菌株的异性传播的性传染病模型.得到了边界平衡点稳定的充要条件,并确认在边界平衡点的稳定性和正平衡点的存在性之间存在着很强的联系.但是只给出了特殊条件下正平衡点稳定的充要条件,这篇文章将就以前没解决的问题,对这类模型给出完整的分析.     

Global dynamics of a delayed predator–prey model with stage structure for the predator and the prey

A delayed predator–prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each feasible equilibrium of the system is discussed, and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of the persistence theory for infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using suitable Lyapunov functions and the LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when both the predator–extinction equilibrium and the coexistence equilibrium do not exist, and that the predator–extinction equilibrium is globally stable when the coexistence equilibrium does not exist. Further, sufficient conditions are obtained for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Coexistence of Two Species in a Strongly Coupled Schoener’s Competitive Model

This paper deals with the existence of positive solution to a strongly coupled system with homogeneous Dirichlet boundary conditions describing a Schoener’s competitive interaction of two species. Making use of the Schauder fixed point theorem, a sufficient condition is given for the system to have a coexistence. And true solutions are constructed based on monotone iterative method. Our results show that this model possesses at least one coexistence state if cross-diffusions and intra-specific competitions are weak.     

Global regulation of individual decision making

Collective behavior of a group of individuals is studied. Each individual adopts one of two alternative decisions on the basis of a neural network bistable dynamical system. The parameters of this system are regulated by collective behavior of the group with the purpose to control the number of individuals with certain decision. It is shown how behavior of the group depends on the distribution of initial states of individuals before they begin the process of decision making. If this distribution is narrow, then it can be impossible to achieve a stable coexistence of two decisions, and oscillations in the number of individuals with given decisions are observed. Various implications of this theory are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamics of virus infection models with density‐dependent diffusion and Beddington–DeAngelis functional response

In this work, we integrate both density‐dependent diffusion process and Beddington–DeAngelis functional response into virus infection models to consider their combined effects on viral infection and its control. We perform global analysis by constructing Lyapunov functions and prove that the system is well posed. We investigated the viral dynamics for scenarios of single‐strain and multi‐strain viruses and find that, for the multi‐strain model, if the basic reproduction number for all viral strains is greater than 1, then each strain persists in the host. Our investigation indicates that treating a patient using only a single type of therapy may cause competitive exclusion, which is disadvantageous to the patient's health. For patients infected with several viral strains, the combination of several therapies is a better choice. Copyright © 2017 John Wiley & Sons, Ltd.     

Two patterns of recruitment in an epidemic model with difference in immunity of individuals

In this paper, two SIR epidemic models with different patterns of recruitment and difference in immunity are investigated. When the recruitment rate is less than some threshold value, the disease will be eradicated. Furthermore, for the continuous recruitment model, according to the Poincare–Bendixson theorem, the global asymptotical stability of a unique positive equilibrium is obtained. For the pulse recruitment model, we investigated the existence of nontrivial periodic solutions via a supercritical (subcritical) bifurcation. From a biological point of view, our results indicate that (1) the disease can be eradicated if the recruitment rate is controlled under some threshold; (2) the number of the infected increases as the difference in immunity increases; (3) fewer individuals are infected as the pulse recruitment is taken, displaying its effect on the control of the disease.