The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population

Seasonal changes in temperature, humidity, and rainfall affect vector survival emergence of mosquitoes thus impact the dynamics vector-borne disease outbreaks. Recent studies deterministic stochastic epidemic models with periodic environments have shown that average basic reproduction number is not sufficient to predict an outbreak. We extend these time-nonhomogeneous dengue demographic variability wherein adult vectors emerge from larval stage vary periodically. The combined effects periodicity provide a better understanding risk A multitype branching process approximation model near disease-free solution used calculate probability follows system differential equations derived backward Kolmogorov equation. This shows outbreak also depends on particular time initial infected individuals. Numerical examples are explored demonstrate estimates approximations agree well continuous-time Markov chain. In addition, we propose simple account for environmental stage.