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

温度，湿度和降雨的季节性变化会影响媒介的生存和蚊子的出现，从而影响媒介传播的疾病暴发的动态。具有周期性环境的确定性和随机流行病模型的最新研究表明，平均基本繁殖数量不足以预测暴发。我们将这些研究扩展到具有人口统计学变异性的时间非均质随机登革热模型，其中从幼虫阶段出现的成年载体周期性变化。变异性和周期性的综合影响可更好地了解登革热暴发的风险。在无病周期解附近的随机登革热模型的多类型分支过程近似值用于计算疾病暴发的可能性。该近似值来自从反向Kolmogorov微分方程派生的微分方程组的解。这种近似表明，疾病暴发的风险也是周期性的，并且取决于特定时间和最初感染个体的数量。数值例子进行了探索，以证明从分支过程的近似值估计爆发概率与连续时间马尔可夫链的估计吻合得很好。此外，我们提出了一个简单的随机模型来说明环境变异性对幼虫期成虫的出现的影响。这种近似表明，疾病暴发的风险也是周期性的，并且取决于特定时间和最初感染个体的数量。数值例子进行了探索，以证明从分支过程的近似值估计爆发概率与连续时间马尔可夫链的估计吻合得很好。此外，我们提出了一个简单的随机模型来说明环境变异性对幼虫期成虫的出现的影响。这种近似表明，疾病暴发的风险也是周期性的，并且取决于特定时间和最初感染个体的数量。数值例子进行了探索，以证明从分支过程的近似值估计爆发概率与连续时间马尔可夫链的估计吻合得很好。此外，我们提出了一个简单的随机模型来说明环境变异性对幼虫期成虫的出现的影响。