The effects of seasonality on disease invasion and superinfection are investigated in dengue epidemic models with two viral strains. A two-strain host–vector nonautonomous ODE is formulated with seasonal periodicity in either vector recruitment or transmission. The basic reproduction number is derived and the dynamics of the single-strain periodic subsystem are summarized. Conditions for uniform persistence and existence of a single-strain periodic solution are verified and the invasion reproduction number is derived. A time-nonhomogeneous, continuous-time Markov chain (CTMC) is formulated from the ODE framework. The basic and invasion reproduction numbers apply to the ODE and CTMC. In the case of invasion, after one strain is established and the invasion reproduction number exceeds one, the ODE predicts a successful invasion, but in the CTMC, there is a periodic probability of invasion that depends on time and size of the invasion. A multitype branching process approximation of the CTMC provides an analytical method to predict the periodic probability of invasion. The numerical results show that the peak time of invasion is related to the current endemic strain and the dominant seasonal driver but it often precedes the peak time of the seasonal driver.

在使用两种病毒株的登革热流行模型中研究了季节性对疾病入侵和重复感染的影响。双菌株宿主-载体非自主 ODE 是在载体招募或传播中具有季节性周期性的。推导了基本再生数并总结了单菌株周期子系统的动力学。验证了单株周期解的一致持续性和存在性的条件，并推导了入侵繁殖数。时间非齐次、连续时间马尔可夫链（CTMC）是根据 ODE 框架制定的。基本再生数和侵入再生数适用于 ODE 和 CTMC。在入侵的情况下，建立一个菌株并且入侵繁殖数超过1后，ODE预测入侵成功，但在CTMC中，入侵的周期性概率取决于入侵的时间和规模。CTMC的多类型分支过程近似提供了预测入侵周期概率的分析方法。数值结果表明，入侵高峰时间与当前流行菌株和主要季节性驱动因素有关，但通常先于季节性驱动因素的高峰时间。