Mathematical modeling and optimal control strategy for a discrete-time Malaria transmission model with vector dynamics

Articles in Press

Document Type : Research Article

Authors

Abdelfatah Kouidere ^{1, 2}

Issam MINIFI ²

khalid adnaoui ¹

¹ Department of Mathematics, Sidi Bennour Polydisciplinary Faculty, Chouaib Doukkali University, Morocco.

² LAMS, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Morocco.

10.22067/ijnao.2026.97717.1836

Abstract

This paper presents a discrete-time mathematical model to study the transmission dynamics of malaria, incorporating both human and mosquito populations. The human population is divided into five compartments: susceptible ($S_k^h$), exposed ($E_k^h$), infectious ($I_k^h$), treated ($T_k^h$), and recovered ($R_k^h$). The mosquito population is divided into three compartments: susceptible ($S_k^m$), exposed ($E_k^m$), and infectious ($I_k^m$). Our objective is to find the optimal strategy to reduce malaria transmission while minimizing intervention costs. We propose four control strategies: insecticide-treated bed nets ($u_{1,k}$), indoor residual spraying ($u_{2,k}$), antimalarial treatment ($u_{3,k}$), and vector control through larviciding ($u_{4,k}$). The discrete version of Pontryagin's Maximum Principle is used to characterize the optimal controls. Numerical simulations performed using MATLAB demonstrate the effectiveness of the proposed control strategies in reducing disease transmission. The results show that implementing all four controls simultaneously can reduce human infections by up to 75\% and mosquito populations by 70\%, providing valuable insights for public health policymakers in malaria-endemic regions.

Keywords

Malaria transmission

Discrete-time model

Vector dynamics

Optimal control, Pontryagin&rsquo

s Maximum Principle

Epidemiological modeling,

Compartmental model

Subjects

• Optimal Control

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