Abstract
Zoonotic infectious diseases are spread from animals to humans. It is estimated that over 60% of human infectious diseases are zoonotic and 75% of them are emerging zoonoses. The majority of emerging zoonotic infectious diseases are caused by viruses including avian influenza, rabies, Ebola, coronaviruses and hantaviruses. Spillover of infection from animals to humans depends on a complex transmission pathway, which is influenced by epidemiological and environmental processes. In this investigation, the focus is on direct transmission between animals and humans and the effects of seasonal variations on the transmission and recovery rates. Fluctuations in transmission and recovery, besides being influenced by physiological processes and behaviors of pathogen and host, are driven by seasonal variations in temperature, humidity or rainfall. A new time-nonhomogeneous stochastic process is formulated for infectious disease spread from animals to humans when transmission and recovery rates are time-periodic. A branching process approximation is applied near the disease-free state to predict the probability of the first spillover event from animals to humans. This probability is a periodic function of the time when infection is introduced into the animal population. It is shown that the highest risk of a spillover depends on a combination of animal to human transmission, animal to animal transmission and animal recovery. The results are applied to a stochastic model for avian influenza with spillover from domestic poultry to humans.