A stochastic SIR influenza vertical transmission model is examined in this paper where vaccination and an incidence rate that is not linear are considered. To determine whether testosterone regulates lower sintering HPA axis function in males, we used a stochastic SIR epidemic procedure with divergent influences on ACTH and cortisol. The suppressive effects on cortisol can be attributed to a peripheral (adrenal) locus. Following that, we came to the conclusion that experimental solutions have been discovered and the requisite statistical findings have been examined. Finally, we deduce that the given mathematical model and the results are relevant to medical research. In the future, this research can be further extended to simulate more results in the medical field.