Sensitivity and optimal control analysis of malaria vaccination model with variable controls

Alphablondy Achieng; Charles Wachira; Benjamin Kikwai

doi:10.51867/asarev.3.1.16

Authors

Alphablondy Achieng Department of Mathematics and Statistics, Machakos University, Kenya Author https://orcid.org/0009-0005-1978-8314
Charles Wachira Department of Mathematics and Statistics, Machakos University, Kenya Author https://orcid.org/0000-0003-1415-2905
Benjamin Kikwai Department of Mathematics and Statistics, Machakos University, Kenya Author https://orcid.org/0000-0002-6741-5011

DOI:

https://doi.org/10.51867/asarev.3.1.16

Keywords:

Optimal Control Analysis, Reproduction Number, Sensitivity

Abstract

In this study a non-linear deterministic malaria vaccination model with optimal control is developed
and analyzed. This improves a recent mathematical model for malaria with standard incidence
by adding sensitivity analysis and optimal controls, where the goal is to obtain optimal control
strategies through vaccination, treatment and personal protection with the aim of minimizing
the number of infections in the population as well as treatment cost. The vaccine reproductive
number Rv is computed using next generation matrix approach. Sensitivity analysis of Rv is
conducted to identify the most influential parameters to be vaccine efficacy (ϵ), vaccination rate (α),
mosquito biting rate (ϕ) and the natural death rate of the mosquitoes (µv). Maximum Principle
of Pontryagin is applied to find the optimal control conditions of treatment efforts, vaccination
efforts, and personal protection efforts on malaria transmission. The numerical simulations show
that, combining control interventions strategies such as treatment efforts, vaccination efforts, and
personal protection efforts such as (spraying of insecticides, use of mosquito treated bed nets,
clearing of bushes and draining stagnant water around the homesteads etc) are necessary for the
reduction of malaria. This study will help the policy makers in deducing control strategies such as
increasing vaccination using vaccines of higher efficacy, increasing treatment and personal protection
efforts for eradication of malaria infection.

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