Numerical Simulation and Sensitivity Analysis of COVID-19 Transmission Involves Virus in the Environment

Abstract

This paper is aimed to develop a new COVID-19 mathematical model involving viruses in the environment. In this mathematical model, the human population is divided into five subpopulations: susceptible, exposed, infected, hospitalized, and cured individuals. In addition, the model also contains the virus population in the environment. Infection in the model occurs due to interactions between susceptible individual subpopulations and infected individuals and hospitalizations, as well as the spread of the virus in the environment. Based on the results of dynamic analysis, this model has two equilibrium points, the disease-free and endemic equilibrium points. The disease-free equilibrium point always exists, and both equilibrium points are locally asymptotically stable if they meet the Routh-Hurwitz criteria. Model sensitivity analysis was carried out on model parameters that affect the basic reproduction number with the most sensitive parameters are the natural death rate, the recruitment rate, the transmission rate of the virus in the environment, the virus clearance rate, and the rate of wearing PPE (Personal Protective Equipment), as well as the parameter that does not affect the basic reproduction number that is the rate of leaving the recovered population. Numerical simulations performed show results in accordance with the analysis, also from the simulations can be concluded that the increase (or decrease) of the transmission rate of the virus in an environment that has a higher sensitivity index has more significant influences on the basic reproduction number and the number of infected population than the transmission rate of hospitalized individuals.

Keywords: Basic Reproduction Number, Dynamics Analysis, Epidemic Models of COVID-19, Local Stability Analysis, Sensitivity Analysis.