## <演講公告>美國德州理工大學張瑞珍教授-線上演講

**Sophia Jang/ (Professor, Department of Mathematics and Statistics, ****Texas Tech University, USA)**

時 間： 110 年 6 月 16日 (星期四) 13:10-14:00

地 點：視訊演講

如要加入這場視訊會議，請按一下這個連結：https://meet.google.com/ixc-wrmv-ijz

你也可以透過電話加入通話，只要撥打 +1 615-640-0129，然後輸入以下 PIN 碼即可：597 058 325#

**Title**: The role of host refuge and strong Allee effects in a host--parasitoid system

**Abstract**

In this talk, we will discuss a discrete host-parasitoid model of difference equations with a spatial host refuge where the hosts in the refuge patch are free from parasitism but undergo a demographic strong Allee effect. If the growth rate of hosts in the non-refuge patch is less than one, a host Allee threshold is derived below which both populations become extinct. It is proven that both populations can persist indefinitely if the host growth rate in the non-refuge patch exceeds one and the maximum reproductive number of parasitoids is greater than one. Numerical simulations reveal that the host refuge can either stabilize or destabilize the host-parasitoid interactions, depending on other model parameters. A large number of parasitoid turnover from a parasitized host may be detrimental to the parasitoids due to Allee effects in the hosts within the refuge patch. Moreover, it is demonstrated numerically that if the host growth rate is not small, the population level of parasitoids may suddenly reduce to a small value as some parameters are varied.

**Sophia Jang/ (Professor, Department of Mathematics and Statistics, ****Texas Tech University, USA)**

時 間： 110 年 6 月 16日 (星期四) 14:10-15:00

地 點：視訊演講

如要加入這場視訊會議，請按一下這個連結：https://meet.google.com/ixc-wrmv-ijz

你也可以透過電話加入通話，只要撥打 +1 615-640-0129，然後輸入以下 PIN 碼即可：597 058 325#

**Title**: Invasion and superinfection in a two-strain dengue epidemic model with demographic and seasonal variation

**Abstract**

The effects of seasonality on disease invasion and superinfection will be introduced for a dengue epidemic model with two viral strains. The host-vector ODE model includes seasonal variations in transmission and vector recruitment rates through periodic parameters. We will derive the basic reproduction number of the two-strain nonautonomous ODE model and study the dynamics of the single-strain periodic subsystem. We will verify uniform persistence and existence of a single-strain periodic solution when the basic reproduction number exceeds one. Assuming the single strain 1 periodic solution is locally stable, we derive the invasion reproduction number for the second strain. The periodic ODE system is then generalized to a time-nonhomogeneous continuous-time Markov chain (CTMC) model. The invasion reproduction number of the nonautonomous ODE model serves as a threshold for invasion in the ODE and CTMC models. If the invasion reproduction number is greater than one, then there is a successful invasion in the ODE system but there is only a positive probability of invasion in the CTMC model as invasion may not occur. A multitype branching process approximation of the CTMC model is used to estimate the probability of invasion of the second strain. It is demonstrated numerically that the branching process estimate of the probability of invasion is periodic and depends on the time and the number of invading infected hosts or vectors that are introduced. Several numerical examples illustrate that the branching process estimates for probabilities of invasion are in good agreement with simulations of the CTMC model. It is shown that superinfection with seasonality in recruitment and transmission rates can either increase or decrease the probability of an invasion of a second strain as compared to a constant environment.