Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

In this paper, we study the spreading of infections in complex heterogeneous networks based on an SIRS epidemic model with birth and death rates. We find that the dynamics of the network-based SIRS model is completely determined by a threshold value. If the value is less than or equal to one, then the disease-free equilibrium is globally attractive and the disease dies out. Otherwise, the disease-free equilibrium becomes unstable and in the meantime there exists uniquely an endemic equilibrium which is globally asymptotically stable. A series of numerical experiments are given to illustrate the theoretical results. We also consider the SIRS model in the clustered scale-free networks to examine the effect of network community structure on the epidemic dynamics.     

流行性传染病动力学模型的近似解

研究了一类流行性传染病.描述了传播动力学的生态模型.利用同伦映射理论和方法,得到了相应模型的近似解.     

Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays

In this paper, we study a new SVEIRS infectious disease model with pulse and two time delays. The pulse vaccination strategy is used as an effective strategy for the elimination of infectious disease. The model consists of a set of integro-differential equations. The existence and global attractivity of ‘infection-free’ periodic solution, permanence of an endemic model are investigated.     

Global attractivity and permanence of a delayed SVEIR epidemic model with pulse vaccination and saturation incidence

In this study, we formulate and analyze a new SVEIR epidemic disease model with time delay and saturation incidence, and analyze the dynamic behavior of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive for some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. By computer simulation it is concluded that a large vaccination rate or a short pulse of vaccination or a long latent period are each a sufficient condition for the extinction of the disease.     

Optimal control of a vector borne disease with horizontal transmission

The paper presents the optimal control applied to a vector borne disease with direct transmission in host population. First, we show the existence of the control problem and then use both analytical and numerical techniques to investigate that there are cost effective control efforts for prevention of direct and indirect transmission of disease. In order to do this three control functions are used, one for vector-reduction strategies and the other two for personal (human) protection and blood screening, respectively. We completely characterize the optimal control and compute the numerical solution of the optimality system using an iterative method.     

Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population

In this paper, we propose a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population, which is derived from the continuous case by using the well-known backward Euler method and by applying a Lyapunov function technique, which is a discrete version of that in the paper by Prüss et al. [J. Prüss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. Ser. B 6 (2006) 225-235]. It is shown that the global dynamics of this discrete epidemic model with latency are fully determined by a single threshold parameter.     

Epidemic spreading on networks with overlapping community structure

Many real networks are characterized by overlapping community structures in which vertices may belong to more than one community. In this paper, we propose a network model with overlapping community structure. The analytical and numerical results show that the connectivity distribution of this network follows a power law. We employ this network to investigate the impact of overlapping community structure on susceptible-infected-susceptible (SIS) epidemic spreading process. The simulation results indicate that significant overlapping community structure results in a major infection prevalence and leads to a peak of the spread velocity in the early stages of the emerging infection.     

Mathematical Analysis of SIR Epidemic Model with Piecewise Infection Rate and Control Strategies

The limitation of contact between susceptible and infected individuals plays an important role in decreasing the transmission of infectious diseases. Prevention and control strategies contribute to minimizing the transmission rate. In this paper, we propose SIR epidemic model with delayed control strategies, in which delay describes the response and effect time. We study the dynamic properties of the epidemic model from three aspects: steady states, stability and bifurcation. By eliminating the existence of limit cycles, we establish the global stability of the endemic equilibrium, when the delay is ignored. Further, we find that the delayed effect on the infection rate does not affect the stability of the disease-free equilibrium, but it can destabilize the endemic equilibrium and bring Hopf bifurcation. Theoretical results show that the prevention and control strategies can effectively reduce the final number of infected individuals in the population. Numerical results corroborate the theoretical ones.