Dynamics of a Diffusion Malaria Model With Vector-Bias北大核心CSCD

为了探讨季节性、蚊子叮咬的偏好性和人类的扩散对疟疾传播的影响,该文提出了一个部分退化的周期反应扩散模型.利用动力系统的持续性理论,研究了模型关于基本再生数R₀的阈值动力学.即当R₀<1时,疾病灭绝;而当R₀>1时,疾病一致持续,且会发生季节性的流行.数值上发现了忽略空间异质性和蚊子叮咬的偏好性会低估疾病传染的风险.     

How does within‐host dynamics affect population‐level dynamics? Insights from an immuno‐epidemiological model of malaria

Malaria is one of the most common mosquito‐borne diseases widespread in the tropical and subtropical regions. Few models coupling the within‐host malaria dynamics with the between‐host mosquito‐human dynamics have been developed. In this paper, by adopting the nested approach, a malaria transmission model with immune response of the host is formulated. Applying age‐structured partial differential equations for the between‐host dynamics, we describe the asymptomatic and symptomatic infectious host population for malaria transmission. The basic reproduction numbers for the within‐host model and for the coupled system are derived, respectively. The existence and stability of the equilibria of the coupled model are analyzed. We show numerically that the within‐host model can exhibit complex dynamical behavior, possibly even chaos. In contrast, equilibria in the immuno‐epidemiological model are globally stable and their stabilities are determined by the reproduction number. Increasing the activation rate of the within‐host immune response “dampens” the sensitivity of the population level reproduction number and prevalence to the increase of the within‐host reproduction of the pathogen. From public health perspective this means that treatment in a population with higher immunity has less impact on the population‐level reproduction number and prevalence than in a population with less immunity.     

A West Nile Virus Model with Vertical Transmission and Periodic Time Delays

Seasonal change has played a critical role in the evolution dynamics of West Nile virus transmission. In this paper, we formulate and analyze a novel delay differential equation model, which incorporates seasonality, the vertical transmission of the virus, the temperature-dependent maturation delay and the temperature-dependent extrinsic incubation period in mosquitoes. We first introduce the basic reproduction ratio $$R_0$$ for this model and then show that the disease is uniformly persistent if $$R_0>1$$. It is also shown that the disease-free periodic solution is attractive if $$R_0<1$$, provided that there is only a small invasion. In the case where all coefficients are constants and the disease-induced death rate of birds is zero, we establish a threshold result on the global attractivity in terms of $$R_0$$. Numerically, we study the West Nile virus transmission in Orange County, California, USA.     

Asymptotic behavior of the principal eigenvalue and the basic reproduction ratio for periodic patch models

Science China Mathematics - This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and the basic reproduction ratio associated with periodic population models in...     

Threshold dynamics for a cholera epidemic model with periodic transmission rate

A cholera epidemic model with periodic transmission rate is presented. The basic reproduction number is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the cholera eventually disappears if the basic reproduction number is less than one. And if the basic reproduction number is greater than one, there exists a positive periodic solution which is globally asymptotically stable. Numerical simulations are provided to illustrate analytical results.     

Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects

In this article the minimum number of positive periodic solutions admitted by a non-autonomous scalar differential equation is estimated. This result is employed to find the minimum number of positive periodic solutions admitted by a model representing dynamics of a renewable resource that is subjected to Allee effects in a seasonally varying environment. The Allee effect refers to a decrease in population growth rate at low population densities. Leggett–Williams multiple fixed point theorem is used to establish the existence of positive periodic solutions.     

Global analysis of multi-strains SIS, SIR and MSIR epidemic models

We consider SIS, SIR and MSIR models with standard mass action and varying population, with n different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each strain a basic reproduction ratio can be associated. It corresponds to the case where only this strain exists. The basic reproduction ratio of the complete system is the maximum of each individual basic reproduction ratio. Actually we also define an equivalent threshold for each strain. The winner of the competition is the strain with the maximum threshold. It turns out that this strain is the most virulent, i.e., this is the strain for which the endemic equilibrium gives the minimum population for the susceptible host population. This can be interpreted as a pessimization principle.     

Three kinds of TVS in a SIR epidemic model with saturated infectious force and vertical transmission

Three different vaccination and treatment strategies in the SIR epidemic model with saturated infectious force and vertical transmission are analyzed. The dynamics of epidemic models are globally investigated by using Floquet theory and comparison theorem of impulsive differential equation. Thresholds are identified and global stability results are proved. For every treatment and vaccination strategy, the disease-free periodic solution of impulsive system has been obtained and is found to be globally asymptotically stable when the basic reproduction number is less than one, equivalently the cure rate is larger than the threshold value, whereas the disease is persistent when the basic reproduction number is larger than one. These results indicate that a large cure rate will lead to the eradication of a disease.     

Basic Reproduction Number of Rabies Model with Stage Structure

The mathematical model is proposed to simulate the dynamics of rabies transmissions in the raccoon population where juveniles stay with their mother and become adults until they establish their own habitats. The basic reproduction number of rabies transmission is formulated and is shown to be a threshold value of disease invasion. The bifurcation direction from the disease-free equilibrium is proved to be forward when the basic reproduction number passes through unity for spatial homogenous environment. The global stability of the disease-free steady state is also studied.     

Mathematical analysis and application of a cholera transmission model with waning vaccine-induced immunity

In this paper, a cholera infection model with vaccination is investigated, in which hyperinfectious and hypoinfectious vibrios, both human-to-human and environment-to-human transmission pathways, and waning vaccine-induced immunity are considered. The basic reproduction number is calculated and verified to be a threshold determining the global dynamics of the model. In addition, an application is demonstrated by investigating the cholera outbreak in Somalia, and the relevant control measures in the short term are given by elasticity and sensitivity analysis.     

Evolutionary dynamics of a system with periodic coefficients

We investigate a problem in evolutionary game theory based on replicator equations with periodic coefficients. This approach to evolution combines classical game theory with differential equations. The RPS (Rock-Paper-Scissors) system studied has application to the population biology of lizards and to bacterial dynamics. The presence of periodic coefficients models variations in the environment due to seasonal effects and results in parametric excitation which is studied through the use of perturbation series and numerical integration.     

Dynamics of an age‐structured host‐vector model for malaria transmission

In this paper, we propose a host‐vector model for malaria transmission by incorporating infection age in the infected host population and nonlinear incidence for transmission from infectious vectors to susceptible hosts. One novelty of the model is that the recovered hosts only have temporary immunity and another is that successfully recovered infected hosts may become susceptible immediately. Firstly, the existence and local stability of equilibria is studied. Secondly, rigorous mathematical analyses on technical materials and necessary arguments, including asymptotic smoothness and uniform persistence of the system, are given. Thirdly, by applying the fluctuation lemma and the approach of Lyapunov functionals, the threshold dynamics of the model for a special case were established. Roughly speaking, the disease‐free equilibrium is globally asymptotically stable when the basic reproduction number is less than one and otherwise the endemic equilibrium is globally asymptotically stable when no reinfection occurs. It is shown that the infection age and nonlinear incidence not only impact on the basic reproduction number but also could affect the values of the endemic steady state. Numerical simulations were performed to support the theoretical results.     

Global analysis of a multi-group animal epidemic model with indirect infection and time delay

The transmission mechanism of some animal diseases is complex because of the multiple transmission pathways and multiple-group interactions, which lead to the limited understanding of the dynamics of these diseases transmission. In this paper, a delay multi-group dynamic model is proposed in which time delay is caused by the latency of infection. Under the biologically motivated assumptions, the basic reproduction number $R_0$ is derived and then the global stability of the disease-free equilibrium and the endemic equilibrium is analyzed by Lyapunov functionals and a graph-theoretic approach as for time delay. The results show the global properties of equilibria only depend on the basic reproductive number $R_0$: the disease-free equilibrium is globally asymptotically stable if $R_0\leq 1$; if $R_0>1$, the endemic equilibrium exists and is globally asymptotically stable, which implies time delay span has no effect on the stability of equilibria. Finally, some specific examples are taken to illustrate the utilization of the results and then numerical simulations are used for further discussion. The numerical results show time delay model may experience periodic oscillation behaviors, implying that the spread of animal diseases depends largely on the prevention and control strategies of all sub-populations.     

Modeling the spatiotemporal variations in brucellosis transmission

In this paper, we propose a nonlinear modeling framework to investigate the transmission dynamics of brucellosis, incorporating both the spatial and seasonal variations. The spatial modeling is based on a patch structure, and the seasonal impact is represented by utilizing time-periodic model parameters. We demonstrate this framework through a two-patch model and conduct detailed analysis, for the cases with and without seasonal oscillations, respectively. In particular, we establish the threshold dynamics results using the reproduction numbers defined under different scenarios. Our findings underscore the importance of including spatial and seasonal heterogeneities in the design of control strategies for brucellosis.     

Backward/Hopf bifurcations in SIS models with delayed nonlinear incidence rates

The classical SIS model with a constant transmission rate exhibits simple dynamic behaviors fully determined by the basic reproduction number. Behavioral changes and intervention measures influenced by the level of infection, likely with a time lag, require the transmission rate to be a nonlinear function of the total infectives. This nonlinear transmission, as shown in this paper via a combination of qualitative and numerical analysis, can generate interesting dynamical behaviors at the population level including backward and Hopf bifurcations. We conclude that sustained infections and periodic outbreaks can be consequences of delayed changes in behaviors or human intervention.      

Basic Reproduction Number in a Growing Population

The basic reproduction number of a fast disease epidemic on a slowly growing network may increase to a maximum then decrease to its equi- librium value while the population increases, which is not displayed by classical homogeneous mixing disease models. In this paper, we show that, by properly keeping track of the dynamics of the per capita contact rate in the population due to population dynamics, classical homogeneous mixing models show simi- lar non-monotonic dynamics in the basic reproduction number. This suggests that modeling the dynamics of the contact rate in classical disease models with population dynamics may be important to study disease dynamics in growing populations.     

Global stability of a delayed epidemic model with latent period and vaccination strategy

In this paper, a mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period and waning vaccine-induced immunity is investigated. The basic reproduction number is found by applying the method of the next generation matrix. It is shown that the global dynamics of the model is completely determined by the basic reproduction number. By means of appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proven that if the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable and the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic.     

一类具有双线性传染率的HIV/AIDS病毒动力学改进模型

针对HIV/AIDS传播的具有常数移民和指数出生的SI型模型,为了更加符合实际意义,对具有双线性传染率的模型进行局部改进,并对改进后的动力学模型进行了简化.对于改进后的模型,证明了平衡点的存在与局部稳定性,并证明了传染病毒的灭绝与持续性,得到了传染病毒的基本再生数.结果表明:当单位时间内从外界迁入人口中染病者的比例系数c近似等于零时,基本再生数小于1时,传染病毒最终灭绝;当基本再生数大于1时,模型存在唯一的正平衡点,且是局部渐近稳定的,说明传染病毒一致持续存在.     

一类带有治愈率的HIV感染的CD4＋T细胞模型的动力学性质

本文主要介绍一类带有治愈率的HIV感染的CD4 T细胞模型的动力学性质,同时证明了如果基本再生数R0＜1,HIV感染消失;如果R0＞1,HIV感染持续.然后进行数值模拟,给出了地方性平衡点E·全局稳定的参数域,得到了地方性平衡点E·不稳定时周期解存在.     

Dynamics of a generalized predator‐prey model with delay and impulse via the basic reproduction number

In this paper, we study a generalized predator‐prey model with delay and impulse. The existence of the predator‐free periodic solution is investigated. We employ the approach and techniques coming from epidemiology and calculate the basic reproduction number for the predator. Using the basic reproduction number, we consider the global attraction of the predator‐free periodic solution and permanence of the model. As for application, an example is discussed. Furthermore, some numerical simulations are given to illustrate our results.