Analysis and dynamics of measles with control strategies: a mathematical modeling approach

In this work, we examine the impact of certain preventive measures for effective measles control. To do this, a mathematical model for the dynamics of measles transmission is developed and analyzed. A suitable Lyapunov function is used to establish the global stability of the equilibrium points. Our analysis shows that the disease-free equilibrium is globally stable, with the measles dying out on the long run because the reproduction number $${\mathcal {R}}_{0}\le 1$$ . The condition for the global stability of the endemic equilibrium is also derived and analyzed. Our findings show that when $${\mathcal {R}}_0> 1$$ , the endemic equilibrium is globally stable in the required feasible region. In this situation, measles will spread across the populace. A numerical simulation was performed to demonstrate and support the theoretical findings. The results suggest that lowering the effective contact with an infected person and increasing the rate of vaccinating susceptible people with high-efficacy vaccines will lower the prevalence of measles in the population.