A mathematical model of malaria transmission dynamics with multi-stage infection and dual treatment pathways - Panca Dewi Fitriyana; Budi Priyo Prawoto (Bulletin of Applied Mathematics and Mathematics Education, 2026)
Malaria remained a complex global public health challenge due to the interplay between biological transmission and human treatment-seeking behavior. This study developed a deterministic mathematical model incorporating two levels of infection severity (mild and severe) and dual treatment pathways, namely herbal and medical treatment. The model was formulated as a system of nonlinear ordinary differential equations and analyzed using the Next Generation Matrix method to derive the basic reproduction number , ​, while local stability was examined using the Routh–Hurwitz criterion. The results showed that the disease-free equilibrium was locally asymptotically stable when , indicating the eventual elimination of the disease. Sensitivity analysis revealed that mosquito mortality and transmission rates were the most influential parameters affecting disease spread. Numerical simulations further demonstrated that increasing early-stage treatment, particularly herbal treatment for mild infections, significantly reduced and limited progression to severe cases. These findings highlighted the critical role of early treatment-seeking behavior combined with effective vector control in reducing malaria transmission and supporting long-term elimination strategies.