The Effect of Lockdown on Mean Persistence Time of Highly Infectious Diseases: A Stochastic Model Based Study

Infectious diseases have become a potential threat to public health over the last decade. This trend is possibly due to the emergence of highly pathogenic infections like Ebola, Influenza, West Nile virus, SARS, and very recently COVID-19, etc. These diseases are affecting the public health and have triggered significant economic damages worldwide. In this present study, we develop a stochastic epidemic model to study the effect of lockdown on infectious disease dynamics. The quarantined and un-quarantined susceptible and symptomatic and asymptomatic individuals are put into separate classes. The rate of susceptible to quarantine and quarantine to susceptible are assumed to be functions of time to capture the non-uniformity in the said two rates during the lockdown phase and unlock phase. These two parameters are also assumed to be dependent on the period of complete lockdown. A new approach termed as maximum stability index is coined to see the effect of the period of complete lockdown on the mean persistence time, which is surprisingly difficult to achieve in case the dimension of the model is high. However, the mean persistence time of the total infected population including symptomatic and asymptomatic cases is obtained by taking the average of the observed time to extinctions based on simulation