Modeling and analysis of the symptomatic and asymptomatic infections of swine flu with optimal control

Abstract

Swine flu is an infectious disease which spreads very rapidly in the population. Infected droplets are expelled into the air by swine flu infected individuals through coughing and sneezing. This disease is transmitted to susceptible individuals by inhalation or ingestion of these infected droplets containing virus. In this paper, we propose and analyze a mathematical model for Swine Flu by considering symptomatic and asymptomatic infections. It is assumed that the transmission rates due to symptomatic and asymptomatic individuals are different. The mathematical model is formulated by assuming simple mass-action type incidence. The basic reproduction number R0 of the model is computed and the local and the global stabilities of different equilibria of the model are studied. Further, this model is extended to optimal control model. The optimal control model is analyzed using Pontryagin’s Maximum Principle and is solved numerically using MATLAB. Finally numerical simulation is performed to see the effect of optimal control on the infected population. It is observed that optimal control model gives better result compared to the model without optimal control as it reduces the number of infectives significantly in a desired interval of time.