A Vaccination-Based Mathematical Model for Reducing Malaria Transmission

Malaria is a mosquito-borne infectious disease affecting humans and other animals, with symptoms including fever, fatigue, vomiting, and headaches, and severe cases can lead to jaundice, seizures, coma, or death. In this seminar work, we developed a mathematical model to study the control of malaria incorporating the effects of vaccination. We investigated the positivity of solutions and established the conditions necessary for the existence and uniqueness of the model. The sensitivity analysis revealed that parameters with positive sensitivity indices, such as the contact rates between susceptible humans and infected mosquitoes, significantly impact the disease's prevalence. Therefore, reducing these contact rates through control measures can mitigate malaria spread. Conversely, the recovery rate (q) has a negative sensitivity index, indicating that increasing the recovery rate via effective vaccination and treatment helps curb malaria transmission. Numerical simulations demonstrated that effective control measures, including high vaccination rate and treatment, lead to a significant decrease in the number of infected individuals and vectors. Specifically, Figs. 3a through 3h showed that the number of susceptible and infected individuals and vectors can be reduced to zero, suggesting that malaria can be effectively controlled and potentially eradicated from the population. We obtained the basic reproduction number (\(\left( {{R_0}} \right)\) and showed that the disease-free equilibrium is locally and asymptotically stable when \({R_0}<1\), indicating that malaria can be eradicated within a finite period.