<p style='text-indent:20px;'>We consider the susceptible-infected-removed (SIR) epidemic model and apply optimal control to it successfully. Here two inputs are considered, so that infection rate is decreased infected individuals removed. Our approach reduce computation of input stable manifold an invariant in a Hamiltonian system. The situation which target equilibrium has center directi...

In this paper we analyze the seasonally forced SIR model. Compared with autonomous model, time dependence adds many difficulties due to complexities of mathematical tools deal with. The absence monotonicity properties and structure equations are marked features that hinder use commonly applied in dynamical systems. Our contribution can be summarized two items. First, provide sufficient conditio...

Lots of real word problems can be motivated and modeled as spreads of epidemics through a network. Prominent examples include the spread of worms and email viruses over the Internet, the spread of disease among the population, and the spread of harmful gossip or panic in a social network. We want to protect computer networks from viruses, prevent disease spreads, and control the leakage of sens...