Is reinfection negligible effect in COVID-19? A mathematical study on the effects of reinfection in COVID-19

Serological studies show that besides the development of suitable antibodies that are evidenced in people who get infected with SARS-CoV2 or in people who are vaccinated, the possibility of getting reinfected with SARS-CoV2 remains non-zero (may be finite). The present article studies how far this possibility of reinfection impacts the transmission dynamics of COVID-19. Considering a six compartment mathematical model, we have studied the transmission dynamics of the disease and presented the situations that will lead to endemic-free (also endemic) state. Considering the COVID-19 waves in India during the spread of SARS-CoV-2, delta variant of SARS-CoV-2, and Omicron variant, the parameters of the model are estimated corresponding to these three situations. As expected, the obtained parameters lie in the stable region of endemic state. The changes in dynamics of the system with the reinfection is studied, and it shows that its effects are not neglible. Even finite value of reinfection can significantly vary the number of infected individuals, and it could explain secondary (smaller) rise in the COVID-19 cases after the COVID-19 wave. We also study the dynamics of the system through fractional order differential equations.