Population dispersal and optimal control of an SEIR epidemic model

This paper formulates and analyses a susceptible-exposed-infected-recovered (SEIR) type epidemic model with the effect of transport-related infection between two cities in the presence of treatment control. The dispersal of populations from one city to another city has an important impact on the dynamics of disease evolution. The basic reproduction number is calculated for all the different cases of the proposed model system. It is found out that the disease-free equilibrium is disease-free if the basic reproduction is less than unity, otherwise the disease may remain in the system. In addition, the optimal control problem is constructed and solved analytically and numerically by considering the treatment control as a control variable. Further, we present a numerical simulation to confirm the analytical results. Finally, we show a comparison of the result of our predicted model with the real data of severe acute respiratory syndrome (SARS) outbreak in 2003 in Hong Kong.