Covid 19, Re-Infection and Its Potential Impact on Economy: A Policy-Based Analysis with Mathemetical Modelling (SIR)

In the wake of temporary stability in the increase of infection numbers of COVID-19 around June / July in 2020, a number of governments have partially or totally lifted the restrictions in haste, aiming to restart the economy as soon as possible. With these policies to restart the economy, second wave of epidemic appears in some western European countries and Canada in October 2020. Meanwhile, more and more multiple twice-infected (re-infected) cases have been reported, suggesting the possible rapid loss of natural immunity to COVID-19. A cross-sectional research is attempted in this paper by developing a mathematical ordinary partial differential equations model (the SIR model) of the COVID-19 epidemic with specific emphasize on the immunity loss, this model is able to simulate different epidemic dynamics by considering different rate of immunity loss and duration of suppression policy. Then I conduct a cost-effective analysis on the suppression policy exit-time problem with different scenarios. Finally, there are discussions on several relevant topics (second wave and vaccination) on COVID-19 based on the simulation results from new SIR model. Overall, the speculations of this paper suggest that policy makers should not relax their vigilance too early, since with re-infection in effect, they could no longer hope for herd immunity, while the threat of a second wave draws near.