OPTIMAL CONTROL ANALYSIS OF THE MALARIA MODEL WITH SATURATED TREATMENT

OPTIMAL CONTROL ANALYSIS OF THE MALARIA MODEL WITH SATURATED TREATMENT

A. K. Srivastav, M. Ghosh

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Abstract

Malaria is a disease which is transmitted through the bite of an infected Anopheles mosquito. According to WHO report, 400.000 people die worldwide from malaria disease annually. We extend a Susceptible-Infective-Susceptible (SIS) model of malaria transmission with saturated treatment to optimal control problem. Pontryagin's Maximum Principle is used to study this optimal control problem and to derive the necessary conditions for the time dependent optimal control. In this paper we discuss di erent types of strategies to  nd the suitable cost-e ective strategy to reduce the num- ber of malaria infectives in a desired interval of time.

Keywords

Malaria Model, Optimal Control, Pontryagin's Maximum Principle, Numer- ical Simulation.