COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL

In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.

A spatial SIS model with Holling II incidence rate

A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of R0 as well as the diffusion rates of susceptible and infected individuals.We also investigate the effect of diffusion rates on asymptotic profile of EE.Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population N is below a certain level;while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.

Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

The Game-Theoretical Model of Using Insecticide-Treated Bed-Nets to Fight Malaria

Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model

To discuss the impact factors on the spread of infectious diseases,we study a free boundary problem describing a SIS(susceptible-infected-susceptible)model in a heterogeneous environment.Firstly,the existence and uniqueness of the global solution are given.Then the basic reproduction number related to time is defined,and a spreading-vanishing dichotomy of infectious diseases is obtained.The impacts of the diffusion rate of infected individuals,expanding capability,and the scope and scale of initial infection on the spreading and vanishing of infectious disease are analyzed.Numerical simulations are given to show that the large expanding capability is unfavorable to the prevention and control of the disease.

Influential nodes identification in complex networks based on global and local information

Identifying influential nodes in complex networks is essential for network robust and stability,such as viral marketing and information control.Various methods have been proposed to define the influence of nodes.In this paper,we comprehensively consider the global position and local structure to identify influential nodes.The number of iterations in the process of k-shell decomposition is taken into consideration,and the improved k-shell decomposition is then put forward.The improved k-shell decomposition and degree of target node are taken as the benchmark centrality,in addition,as is well known,the effect between node pairs is inversely proportional to the shortest path length between two nodes,and then we also consider the effect of neighbors on target node.To evaluate the performance of the proposed method,susceptible-infected(SI)model is adopted to simulate the spreading process in four real networks,and the experimental results show that the proposed method has obvious advantages over classical centrality measures in identifying influential nodes.

Dynamical analysis of an SIS epidemic model with migration and residence time

Migration can be ciivided into temporary and permanent migration,which is related to the residence time of people in the patch,thus we consider an SIS epidemic model with migration and residence time in a patchy environment.If R0≤1,the disease-free equilibrium is globally asymptotically stable and the disease dies out.With the same migration rate of susceptible and infectious individuals and without disease-induced death,when R0>1,the endemic equilibrium is unique and globally asymptotically stable.Numerical simulations are carried out to show the effects of residence time and the migration rate on disease prevalence.

Analysis of a fractional-order SIS epidemic model with saturated treatment

In this paper,we propose and analyze a fractional-order SIS epidemic model with the saturated treatment and disease transmission.The existence and uniqueness,nonnegativity and finiteness of solutions for our suggested model have been studied.Different equilibria of the model are found and their local and global stability analyses are also examined.Furthermore,the conditions for fractional backward and fractional Hopf bifurcation are also analyzed in both the commensurate and incommensurate fractional-order model.We study how the control parameter and the order of the fractional derivative play role in local as well as global stability of equilibrium points and Hopf bifurcation.We have demonstrated the analytical results of our proposed model system through several numerical simulations.