An SIRS epidemic model with a modified nonlinear incidence rate is studied, which describes that the infectivity strong at first as emergence of new disease or reemergence an old disease, but then psychological effect will weaken infectivity. Lastly, goes to saturation state result crowding effect. The nonlinearity functional form infection modified, more reasonable biologically. We analyze sta...

We consider the problem of identifying the time-dependent transmission rate from incidence data and from prevalence data in epidemic SIR, SIRS, and SEIRS models. We show closed representation formulas avoiding the computation of higher derivatives of the data or solving differential equations. We exhibit the connections between the formulas given in several recent papers. In particular we expla...

Mathematical models of disease propagation have been studied for a long time, and various models have been proposed. In the last decade, much attention has been paid to the epidemic dynamics on a network, and those researches have revealed that the network structure affects the epidemic dynamics on the network. Similarly, the spreading of an infectious disease on the network can have a strong e...

To predict the spread of Avian Influenza we propose a synchronous Susceptible-Infected-Recovered-Susceptible (SIRS) Boolean network of poultry farms, using probabilistic Boolean rules. Gravity models from transportation theory are used for the probability of infection of a node in one time step, taking into account farm sizes, distances between farms, and mean distance travelled by birds. Basic...