This paper is concerned with the conditions of existence and nonexistence traveling wave solutions (TWS) for a class discrete diffusive epidemic model. We find that TWS determined by so-called basic reproduction number critical speed: When $$\mathfrak {R}_0>1$$ , there exists speed $$c^*>0$$ such each $$c \ge c^*$$ system admits nontrivial $$c<c^*$$ no system. In addition, boundary asymptotic b...

We study the behavior of epidemic spreading in networks, and, in particular, scale free networks. We use the Susceptible–Infected–Removed (SIR) epidemiological model. We give simulation results for the dynamics of epidemic spreading. By mapping the model into a static bond-percolation model we derive analytical results for the total number of infected individuals. We study this model with vario...

Understanding the spread of infectious disease is an important issue in order to prevent major outbreaks. In this report mathematical modeling is used to gain insight into the dynamics of an epidemic. A process model, the SIR model, exploiting knowledge about population dynamics serves as framework. Key interest is in adapting the stochastic model to observed data – especially from animal produ...

We have described a SIR simulation model for the influenza AH1N1 virus including variable population, periodic transmission coefficient and constant vaccination rate for any age and time. Also, it has been considered the natural mortality rate due to the infection. We analyze the model by means of simulations using several scenarios. The epidemic threshold, that is time and seasonality dependen...

Modelling and simulation of infectious diseases help to predict the likely outcome of an epidemic. A well-known generic model type for the quantitative description of the epidemic evolution dynamics by an ordinary differential equation is provided by so-called SIR models. These models classify a population into “suscepti-ble” (S), “infected” (I) and “recovered” (R) subgroups. One very early and...

We study the global behavior of a non-linear susceptible-infectious-removed (SIR)-like epidemic model with a non-bilinear feedback mechanism, which describes the influence of information, and of information-related delays, on a vaccination campaign. We upgrade the stability analysis performed in d'Onofrio et al. [A. d'Onofrio, P. Manfredi, E. Salinelli, Vaccinating behavior, information, and th...

Based on a theory of population dynamics in perturbed environments, it was hypothesized that measles epidemics can be more efficiently controlled by pulse vaccination, i.e., by a vaccination effort that is pulsed over time (11. Here, we analyze the rationale of the pulse vaccination strategy in the simple SIR epidemic model. We show that repeatedly vaccinating the susceptible population in a se...

Modeling infectious diseases helped out to understand and overcome epidemics. This paper is based on epidemic model SIR, which fits well to many epidemiological diseases. Basic idea of Homotopy Analysis Method (HAM)is discussed and employed to compute an approximation to the solution of nonlinear system of differential equations. The effect of vaccination on the dynamics of childhood disease de...

Discrete-time models, or difference equations, of some well-known SI, SIR, and SIS epidemic models are considered. The discrete-time SI and SIR models give rise to systems of nonlinear difference equations that are similar in behavior to their continuous analogues under the natural restriction that solutions to the discrete-time models be positive. It is important that the entire system be cons...

Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R0 > 1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size o...