Epidemic Dynamics with Nonlinear Incidence Considering Vaccination Effectiveness

This paper presents a mathematical model that examines the effect of nonlinear incidence on disease transmission dynamics. Furthermore, we also accommodate newborn and adult vaccination strategy as the prevention strategy to prevent rapid spread of the disease due to nonlinear incidence rate. Assuming a constant population size, the system is reduced to a two-dimensions and nondimensionalized using the average infectious period as the time scale. Analytical results reveal the existence of both disease-free and endemic equilibria, with the possibility of backward bifurcation when the nonlinear incidence parameter exceeds a critical threshold. This implies that disease persistence may still occur even when the basic reproduction number is less than one. Numerical simulations using MATCONT conducted to visualize the occurrence of both forward and backward bifurcations phenomena. Using COVID-19 parameter values, a global sensitivity analysis via Partial Rank Correlation Coefficient - Latin Hypercube Sampling method indicates that newborn vaccination has a stronger impact on reducing the basic reproduction number. These findings provide important insights for designing effective vaccination strategies and understanding the complex dynamics arising from nonlinear transmission and imperfect immunization.