Abstract The emergence of a widespread infectious disease led to a global health crisis, profound disruptions to health systems, societies, and economies. This study introduces a nonlinear and bilinear incidence function into the infection process within the dynamical system. We develop and analyze an epidemic model structured into compartments for susceptible, exposed, asymptomatic, symptomatic, and recovered individuals. The model is rigorously examined to confirm solution non-negativity and boundedness, identifying disease-free and endemic equilibrium points. The basic reproduction number is derived, followed by stability, sensitivity, and bifurcation analyses to evaluate the influence of key parameters. Model parameters are estimated using real data from four countries to validate the proposed framework. Moreover, an optimal control framework is formulated to limit infection spread, incorporating vaccination of susceptible individuals u₁ (t) and healthcare support u₂ (t) applied to both asymptomatic and symptomatic infected populations.
Swathi et al. (Mon,) studied this question.