Estimating parameter values and initial states of variables in a mathematical model of coronavirus disease 2019 epidemic wave using the least squares method, Visual Basic for Applications, and Solver in Microsoft Excel

Abstract

Background

With the global spread of coronavirus disease 2019 (COVID-19), understanding the mechanisms and characteristics of epidemic waves has become necessary to control its spread. The sixth epidemic wave of COVID-19 in Sapporo, Japan, was analyzed using a new mathematical model called the SI_UI_CI_CPR_UR_C model. The main objectives are (1) introducing the SI_UI_CI_CPR_UR_C model, (2) introducing algorisms by which parameters and initial states were estimated, and (3) estimating values of parameters and initial states, and analyzing the epidemic wave.

Methods

Reported numbers of daily new confirmed infected cases, currently infected cases, and cumulative numbers of recovered or fatal cases were collected from the official website of the city of Sapporo. The SI_UI_CI_CPR_UR_C model, based on susceptible-infectious-removed and infection-period-structured models, was employed. Parameter values and initial states of variables were estimated using the least squares method, Visual Basic for Applications, and Solver in Microsoft Excel.

Results

The peak time of transmission rate was estimated to be 5.8 to 6.0 days after infection, the peak time of infection confirmation rate was 8.0 to 8.1 days after infection, and the ultimate confirmation ratio of infection was 0.65 to 0.85. It was also estimated that almost all individuals in Sapporo were susceptible to the Omicron variant of the severe acute respiratory syndrome-coronavirus 2.

Conclusion

The sixth epidemic wave of COVID-19 was analyzed with the SI_UI_CI_CPR_UR_C model, with which crucial parameters and initial states were estimated. Furthermore, the results indicate that vaccination against the Wuhan strain and the previous infection were insufficient to induce a level of immunity required to prevent infection by the Omicron variant. Further improvement of mathematical modeling for infectious diseases is required to control emerging infectious diseases in the future, even if the threat of COVID-19 is overcome.