Batik Motifs: Dynamic Stability Patterns in a Mathematical Model of Malaria Transmission with Asymptomatic Infection and Superinfection

Abstract

This study discusses the mathematical modeling of malaria transmission, considering the presence of asymptomatic infection and superinfection. The model used is an extension of the SIA-SI (Susceptible–Infected–Asymptomatic in humans and Susceptible–Infected in mosquitoes) model. Each compartment is represented by a system of differential equations based on the principle of the rate of change, reflecting the dynamics of individuals moving between health statuses. An analysis was conducted to determine the disease-free equilibrium and the endemic equilibrium points. The results of the analysis show that in the disease-free state, the entire human and mosquito populations are in a susceptible state with no infected individuals, namely S_h=N_h and S_m=N_m. Meanwhile, the endemic equilibrium occurs when a number of human and mosquito individuals remain infected, depending on infection, recovery, and mortality parameters. This model provides a quantitative overview of the dynamics of malaria transmission and can serve as a basis for formulating more effective disease control strategies.