Modeling the impact of treatment, vaccination and sterile mosquito release on malaria transmission

In this study, we develop and analyze a mathematical model to investigate the effects of treatment, vaccination, and sterile male mosquito release on malaria transmission. The model incorporates different levels of immunity, distinguishing between non-immune and semi-immune populations to better capture the dynamics of malaria spread and control. Using the next-generation matrix method, we compute the control reproduction number and establish the local asymptotic stability of the disease-free equilibrium when $\mathcal{R}_C<1$. A global sensitivity analysis with the reproduction number as the outcome variable is conducted to determine key parameters influencing malaria transmission. Additionally, we formulate and analyze an optimal control problem incorporating vaccination, treatment, and sterile male mosquito release as controls, and carry out a cost-effectiveness analysis to assess the economic feasibility of various intervention strategies. Our results suggest that a comprehensive intervention strategy that integrates treatment, vaccination, and sterile mosquito release is the most effective approach for reducing malaria transmission. However, from a cost-effectiveness perspective, prioritizing vaccination and treatment is the most feasible option in resource-limited settings.