Bio-Mathematics

Measles is a highly contagious, serious airborne disease caused by a virus that can lead to severe complications and death (World Health Organization). Mathematical modeling plays a crucial role in understanding the transmission dynamics of the virus and assessing the impact of control strategies, particularly vaccination and immunity acquired after infection. In this study, we develop and analyze a compartmental epidemiological model that includes several population groups: susceptible (S) individuals, infected (I) individuals, recovered (R) individuals, vaccinated (V ) individuals, and the envi ronment (host of measles virus) (D) individuals. We examine the mathemat ical properties of the model by establishing its positivity and boundedness, determining the disease- free and endemic equilibrium points, and computing the basic reproduction number (R0). Additionaly, we conduct a stability anal ysis to understand the conditions for measles eradication and perform a sensitivity analysis to identify the most inuential parameters a ecting infection dynamics, we conduct numerical simulations using assumed variables, parameter val ues and interpret the results and conduct an optimal control analysis of the model.