Extinction of Disease Pathogenesis in Infected Population and Its Subsequent Recovery: A Stochastic Approach

A stochastic mathematical model of host-pathogen interaction has been developed to estimate the time to extinction of infected population. It has been assumed in the model that the infected host does not grow or reproduce but can recover from pathogenic infection and move to add to the susceptible host population using various drugs or vaccination. Extinction of infected population in host-pathogen interaction depends significantly upon the total population. Here, we consider an extension of our previous work with the stochastic approach to predict the time to extinction of disease pathogenesis. The optimal control approach helped in designing an innovative, safe therapeutic regimen where the susceptible host population enhanced with simultaneous decrease in the infected population. By means of an optimal control theory paradigm, it has also been shown in our preceding research paper that the cost-effective combination of treatment may depend on the population size. In this research paper, we have studied an approximation which is derived in favor of quasi-stationary distribution along with the expected time to extinction for the model of host-pathogen interactions. The complete study has been roofed through the stochastic approach in context that disease pathogenesis is to be extinct and infected population are going to be recovered. Numerical simulation is also done to confirm the analysis.