Exo-SIR: an epidemiological model to analyze the impact of exogenous spread of infection

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc., is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of the virus. First, we present an analytical study. Second, we simulate the Exo-SIR model with and without assuming contact network for the population. Third, we implement the Exo-SIR model on real datasets regarding Covid-19 and Ebola. We found that endogenous infection is influenced by exogenous infection. Furthermore, we found that the Exo-SIR model predicts the peak time better than the SIR model. Hence, the Exo-SIR model would be helpful for governments to plan policy interventions at the time of a pandemic.