Optimal control problem in preventing of swine flu disease transmission

Abstract

Swine flu is a life threatening respiratory disease which originally spread among pigs. The virus easily mutates and is transmitted within human population through coughing or direct contact with infected person. It is caused by type-A influenza virus of subtypes H1N1, H1N2, H3N1, H3N2 and H2N3. The use of proper medical mask has been widely known to protect the user from incoming virus through respiratory transmission. Here in this paper we construct a compartmental SIR dynamical model for swine flu disease transmission. Intervention of transmission is done with the use of medical mask with given rate in each compartment. The problem is represented as an optimal control problem to obtain the optimal control rates. The equilibrium points and basic reproductive ratio as the epidemic indicator before medical mask intervention have shown analytically. Numerical optimal control results are shown to illustrate the effectiveness of the treatment for various parameter values. It is shown that as long as the worsening effect of medical mask not in a high number, then medical mask intervention will reduce swine flu epidemic significantly.