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

Abstract

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.

A stochastic approach for co-evolution process of virus and human immune system

“…In Fig. 3 , real data has been utilized to calibrate the model parameters for the alpha and beta variants of the SARS-CoV-2 virus given by Table 2 , drawing on extensive datasets described in contemporary literature 11 , 35 , 39 – 43 . We have employed the nonlinear least square method for the estimation process.…”

Stability analysis and numerical simulations of the infection spread of epidemics as a reaction–diffusion model

“…However, more compartments must be added to the model to study the spread of COVID‐19. For example, the SEIRUC model was considered in Tamilalagan et al [11] to differentiate between asymptomatic and symptomatic individuals. In Basnarkov [12], the SEAIR model was considered, and stability analysis was performed, among others.…”

“…Based on previous studies on COVID‐19, it has been found that SIR ODE models have limitations and the accuracy of the outcomes can be improved by incorporating spatiotemporal terms in the model equations. Therefore, we consider the model as proposed in Tamilalagan et al [11] with spatiotemporal terms in all model equations. Here, the proposed model consists of six compartments and studies the evolution of COVID‐19‐infected individuals.…”