Optimal (Control of)‎ Intervention Strategies for Malaria Epidemic in Karonga District, Malawi

Abstract EN

Malaria is a public health problem for more than 2 billion people globally.

About 219million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the AfricanRegion despite decades of efforts to control the disease.

Although the disease is preventable, itis life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito.

A deterministic mathematical model with intervention strategies is developed in order toinvestigate the effectiveness and optimal control strategies of indoor residual spraying (IRS),insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria inKaronga District, Malawi.

The effective reproduction number is analytically computed,and the existence and stability conditions of the equilibria are explored.

The model doesnot exhibit backward bifurcation.

Pontryagin’s Maximum Principle which uses both theLagrangian and Hamiltonian principles with respect to a time dependent constant is used toderive the necessary conditions for the optimal control of the disease.

Numerical simulationsindicate that the prevention strategies lead to the reduction of both the mosquito populationand infected human individuals.

Effective treatment consolidates the prevention strategies.

Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infectedpeople.