Persistence and extinction of infection in stochastic population model with horizontal and imperfect vertical disease transmissions

Epidemic models are used to understand the dynamics of disease transmission and explore the possible measures for preventing the spread of infection in the population. Disease transmission is intrinsically random and severely affected by environmental factors. We investigated a stochastic population model of the susceptible-infected-susceptible (SIS) type, in which infection spreads via both vertical and horizontal transmission routes. To incorporate stochasticity to the system, white multiplicative noise was taken into account in the horizontal disease transmission term. We proved that noise intensity, disease transmission, and recovery rates are potential routes for eradicating the disease. Furthermore, the parasite population reduces its fitness for some fixed noise if the relative fecundity of infected hosts and the disease transmission are low. However, if either of these is increased, it observes enhanced fitness. A simulation study illustrated the system's analytically dynamic properties and provided different insights. A case study for the imperfect vertical and horizontal infection transmission is also presented, supporting some of our observed theoretical results.