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Epidemiological models are the mathematical models that capture the dynamicsof epidemics. The spread of the virus has two routes - exogenous andendogenous. The exogenous spread is from outside the population under study,and endogenous spread is within the population under study. Although some ofthe models consider the exogenous source of infection, they have not studiedthe interplay between exogenous and endogenous spreads. In this paper, weintroduce a novel model - the Exo-SIR model that captures both the exogenousand endogenous spread of the virus. We analyze to find out the relationshipbetween endogenous and exogenous infections during the Covid19 pandemic. First,we simulate the Exo-SIR model without assuming any contact network for thepopulation. Second, simulate it by assuming that the contact network is a scalefree network. Third, we implemented the Exo-SIR model on a real datasetregarding Covid19. We found that endogenous infection is influenced by even aminimal rate of exogenous infection. Also, we found that in the presence ofexogenous infection, the endogenous infection peak becomes higher, and the peakoccurs earlier. This means that if we consider our response to a pandemic likeCovid19, we should be prepared for an earlier and higher number of cases thanthe SIR model suggests if there are the exogenous source(s) of infection.

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