Mathematical Exploration of Malaria Transmission Dynamics: Insights from Fractional Models and Numerical Simulation

Abstract

This study presents an innovative mathematical model denoted as the fractional SIP(H)–SI(M) model, which aims to analyze and understand the dynamics of malaria transmission and spread. This model is distinguished by incorporating memory effects through fractional differential equations, allowing for a more accurate and realistic analysis of disease spread compared to traditional models. The proposed model is applied to Algeria by estimating its parameters using recent health data (from 2000). The results revealed that the disease-free equilibrium is stable only when the basic reproduction number is less than one, indicating that controlling the spread of malaria and possibly eradicating it can be achieved by implementing appropriate preventive measures. Simulations also demonstrated a direct correlation between the rate of infection transmission and an increase in the number of infected individuals, highlighting the need for swift action when signs of an outbreak emerge. Based on these findings, a set of preventive measures is recommended, including insecticide spraying programs, widespread distribution of insecticide-treated bed nets, and implementation of effective treatment protocols for infected individuals. This study also emphasizes the importance of continuous monitoring of health data and updating model parameters to ensure the effectiveness and sustainability of preventive measures.