Modelling COVID-19 Transmission in the United States through Interstate and Foreign Travels and Evaluating Impact of Governmental Public Health Interventions

Shah, N. H.; Sheoran, N.; Jayswal, E. N.; Shukla, D.; Shukla, N.; Shukla, J.; Shah, Y.

Background: The first case of COVID-19 was reported in Wuhan, China in December 2019. The disease has spread to 210 countries and has been labeled as a pandemic by WHO. Modelling, evaluating, and predicting the rate of disease transmission is crucial for epidemic prevention and control. Our aim is to assess the impact of interstate and foreign travel and public health interventions implemented by the United States government in response to the Covid-19 pandemic. Methods: A disjoint mutually exclusive compartmental model is developed to study the transmission dynamics of the novel coronavirus. A system of non-linear differential equations was formulated and the basic reproduction number R0 was computed. The stability of the model was evaluated at the equilibrium points. Optimal controls were applied in the form of travel restrictions and quarantine. Numerical simulations were conducted. Results: Analysis shows that the model is locally asymptomatically stable, at endemic and foreigners free equilibrium points. Without any mitigation measures, infectivity and subsequent hospitalization of the population increase while placing interstates individuals and foreigners under quarantine, decreases the chances of exposure and subsequent infection, leading to an increase in the recovery rate. Conclusion: Interstate and foreign travel restrictions, in addition to quarantine, help in effectively controlling the epidemic.