Parameter Estimation of COVID-19 Pandemic Model with Self Protection Behavior Changes

A mathematical model for the transmission dynamics of Coronavirus diseases (COVID-19) is proposed by incorporating self-protection behavior changes in the population. The disease-free equilibrium point is computed and its stability analysis is studied. The basic reproduction number(R0) of the model is computed and the disease-free equilibrium point is locally and globally stable for R0 < 1 and unstable for R0 > 1. Based on the available data the unknown model parameters are estimated using a combination of least square and Bayesian estimation methods for different countries. Using forward sensitivity index the model parameters is carried out to determine and identify the key factors for the spread of disease dynamics. From country to country the sensitive parameters for the spread of the virus varies. It is found out that the reproduction number depends mostly on the infection rates, the threshold value of the force of infection for a population, the recovery rates, and the virus decay rate in the environment. It is also demonstrated that control of the effective transmission rate (recommended human behavioral change towards self-protective measures) is essential to stop the spreading of the virus. Numerical simulations also show that the viruss transmission dynamics depend mostly on those sensitive parameters.