A fractional mathematical model of malaria transmission dynamics with liver stage relapse

Malaria is still a life-threatening disease worldwide, particularly in endemic regions such as Ethiopia. In this study, we develop a mathematical model of malaria transmission dynamics with effective treatment and disease relapse. The model incorporates a hypnozoite compartment representing dormant liver-stage parasites in humans adjacent to the treatment compartment. In the absence of relapse, malaria infections are fully treated and recovered. This model uses the Atangana-Baleanu-Caputo fractional derivative to capture the memory effects of the disease, leading to a more realistic representation than an integer-order model. Our model’s critical parameter values are established by estimating parameters using malaria data from Ethiopia between 2000 and 2023. The findings of a parameter sensitivity analysis on R₀ indicate that reducing human–mosquito contact is essential for controlling transmission. Our results demonstrate the critical role of relapses play in sustaining malaria’s population presence, which complicates eradication attempts. This study emphasizes the value of fractional-order modeling in understanding the complex dynamics of malaria and offers practical insights for policymakers. By focusing on targeted interventions and utilizing historical data, we aim to contribute to the development of more effective strategies for malaria control and management in Ethiopia and similar settings.