Exploring the Dynamics of Malaria in East Nusa Tenggara, Indonesia: Impact of Relapse, Treatment and Vaccination

Malaria infection continues to affect numerous countries worldwide, persisting as a public health issue despite recent progress in control measures. Particularly in regions like Africa and the Middle East, malaria remains a significant concern. We formulate two mathematical models to evaluate how vaccination and treatment efforts contribute to combating malaria. Parameter estimation and model validation are performed using the dataset for malaria incidence from Lembata Regency, East Nusa Tenggara Province, Indonesia. The first model is motivated by the increasing demand for a malaria vaccine. Our study results suggest that such a vaccine could reduce the global prevalence of malaria. The second model includes two types of treatment: radical cure and bloodstream treatments. The model reproduction numbers and equilibrium points for both models are established. A global sensitivity analysis is conducted to identify the parameters that significantly impact the model's reproduction number. Numerical analysis is carried out to support theoretical findings. The extended model results give the necessary malaria control thresholds to lower the $\mathcal{R}^t_c$ value to fully eradicate malaria in Lembata Regency, East Nusa Tenggara Province, Indonesia. Both models demonstrate the vital importance of vaccination and treatment in combating malaria infection.