Optimal Parameter Estimation of Coronavirus Disease Model Based on Gauss-Newton Computational Approach

Abstract

Mathematical modelling of coronavirus disease (COVID-19) is eagerly required in public health to understand the evolution of COVID-19. However, unknown parameters in the model prevent the progress of the modelling. This report aims to study the spread of COVID-19 in Malaysia through the susceptible-infected-recovered (SIR) model. By using the real data of COVID-19 from 1 January to 30 September 2022 to estimate the model parameters, which are the transmission rate and recovery rate, a loss function was introduced. The Gauss-Newton recursion equation was derived and the value of parameters was updated iteratively until convergence was achieved. With these optimal parameter estimates, the SIR model was solved numerically. The model solution revealed that the spread of COVID-19 increased exponentially for the following 2 months. In addition, the prediction results for the coming 16 years show that the number of infected cases will reach a peak of 8.1493 million in 2.5 years. After 10 years, the spread of COVID-19 will stay at a total cumulative of 2.7794, 0.02757 and 2.9857 million for susceptible, infected and recovered cases, respectively. In conclusion, parameter estimation in the SIR model is satisfactorily performed and prediction results of the spread of COVID-19 in Malaysia are clearly interpreted.