Analysis of Optimal Cost-Effectiveness in the COVID-19 Epidemic Model by Considering Quarantine, Hospitalization, and the Environment

In this paper, the population dynamics of a novel coronavirus are studied. An extended SEIR model with quarantine, hospitalization, and the environment compartment is proposed to simulate the novel coronavirus epidemic. The model considers eight distinct epidemiological classes: susceptible, exposed, asymptomatic, symptomatic, quarantined, hospitalized, recovered, and viruses in the environment. The basic reproduction numbers are determined by using a method called the next-generation matrix. The model has two equilibria: a disease-free equilibrium and an endemic equilibrium. The Lyapunov function and the LaSalle invariance principle are used to analyze the global asymptotical stability of the equilibria of the proposed model. The disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity, and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. To study cost-effectiveness assessments for the four optimum control strategies, we ran numerical simulations. When the four control strategies were compared, it was discovered that Strategy A (public health education and intensive medical treatment) was the most economical and efficient control intervention in the absence of vaccination. However, we observe that strategies A, B, and D are similarly effective at containing COVID-19 in terms of infection prevention.