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Exo-SIR: An Epidemiological Model to Analyze the Impact of Exogenous Infection of COVID-19 in India

Epidemiological models are the mathematical models that capture the dynamics of epidemics. The spread of the virus has two routes - exogenous and endogenous. The exogenous spread is from outside the population under study, and endogenous spread is within the population under study. Although some of the models consider the exogenous source of infection, they have not studied the interplay between exogenous and endogenous spreads. In this paper, we introduce a novel model - the Exo-SIR model that captures both the exogenous and endogenous spread of the virus. We analyze to find out the relationship between endogenous and exogenous infections during the Covid19 pandemic. First, we simulate the Exo-SIR model without assuming any contact network for the population. Second, simulate it by assuming that the contact network is a scale free network. Third, we implemented the Exo-SIR model on a real dataset regarding Covid19. We found that endogenous infection is influenced by even a minimal rate of exogenous infection. Also, we found that in the presence of exogenous infection, the endogenous infection peak becomes higher, and the peak occurs earlier. This means that if we consider our response to a pandemic like Covid19, we should be prepared for an earlier and higher number of cases than the SIR model suggests if there are the exogenous source(s) of infection.