Analysis and Numerical Simulation of an Sveirs–Sei Malaria Model with Waning Natural and Vaccine-Induced Immunity

Abstract

Malaria remains a major public-health challenge despite sustained vector-control, treatment, and vaccination efforts. This study formulates and analyzes an eight-compartment SVEIRS–SEI human–mosquito malaria transmission model that explicitly incorporates waning naturally acquired and vaccine-induced immunity.  The basic reproduction number R0, was derived using the next-generation matrix method. Under the baseline parameterization, the model yielded R0=5.604, indicating sustained endemic transmission. Sensitivity analysis identified the mosquito natural death rate as the most influential parameter, with a normalized sensitivity index of −1.073, while the human and mosquito transmission coefficients each had indices of +0.500. Vaccine efficacy showed a negative sensitivity index of −0.191. Numerical simulations demonstrated that increasing vaccine efficacy reduced the peak infectious human population from approximately 780 to 640 individuals, representing about an 18% reduction. Increasing the vaccinated-to-recovered conversion rate reduced the infectious peak from about 800 to 530 individuals, corresponding to approximately a 34% reduction. In contrast, increasing the natural-immunity waning rate raised the infectious-human peak from approximately 630 to more than 1,000 individuals and increased the long-term infectious population from about 50 to nearly 570 individuals. These findings indicate that mosquito survival, transmission intensity, vaccine performance, and persistence of naturally acquired immunity strongly influence malaria dynamics. The model therefore supports integrated malaria-control strategies combining effective vector control, sustained vaccination, and interventions that prolong protective immunity.