Impulsive releases of sterile mosquitoes and interactive dynamics with time delay

Modelling and analysis of periodic impulsive releases of the Nilaparvata lugens infected with wStri-Wolbachia

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild-N . l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild N . l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild N . l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild N . l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions.

Impact of releasing period and magnitude on mosquito population in a sterile release model with delay

Assuming that there are multiple batches of sterile males reared and released during the maturation period, we derive a switching delay differential model to study the fate of wild females under an impulsive and periodic release of sterile males. For the release magnitude of each batch c, we find two threshold values [Formula: see text] and [Formula: see text], and prove that when [Formula: see text], the model admits exactly two periodic solutions, among which one is asymptotically stable and the other is unstable. The trivial equilibrium, corresponding to the elimination of wild females, is locally asymptotically stable, and it becomes globally asymptotically stable when [Formula: see text]. One key step is to prove that every solution is sandwiched between two "good" solutions.

Impulsive release strategies of sterile mosquitos for optimal control of wild population

To investigate the release strategies of sterile mosquitoes for the wild population control, we propose mathematical models for the interaction between two-mosquito populations incorporating impulsive releases of sterile ones. The long-term control model is first studied, and the existence and stability of the wild mosquito-extinction periodic solution are exploited. Thresholds of the release amount and release period which can guarantee the elimination of the wild mosquitos are obtained. Then for the limited-time control model, three different optimal strategies in impulsive control are investigated. By applying a time rescaling technique and an optimization algorithm based on gradient, the optimal impulsive release timings and amounts of sterile mosquitoes are obtained. Our results show that the optimal selection of release timing is more important than the optimal selection of release amount, while mixed optimal control has the best comprehensive effect.

Study of the sterile insect release technique for a two-sex mosquito population model

In this paper, to study the large-scale time control and limited-time control of mosquito population in a field, a two-sex mosquito population model with stage structure and impulsive releases of sterile males is proposed. For the large-scale time control, a wild mosquito-free periodic solution is given and conditions under which it is globally stable are obtained by the use of the monotone system theory. Besides, based on the stability analysis, threshold conditions under which the wild mosquito population is eliminated or not are obtained. Then we study three different optimal release strategies for the limited-time control, which takes into account both of the population control level of wild mosquitoes and the economic input. To solve technical problems in optimal impulsive control, a time rescaling technique is applied and the gradients of cost function with respect to all control parameters are obtained. In addition, by the aid of numerical simulation, we get the optimal release amounts and release timings for each release strategy. Our study indicates that the optimal release timing control is superior to the optimal release amount control. However, simultaneous optimal selection of release amount and release timing leads to the best control performance.

Stability analysis in a mosquito population suppression model

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].

Modeling the suppression dynamics of Aedes mosquitoes with mating inhomogeneity

A novel strategy for controlling mosquito-borne diseases, such as dengue, malaria and Zika, involves releases of Wolbachia-infected mosquitoes as Wolbachia cause early embryo death when an infected male mates with an uninfected female. In this work, we introduce a delay differential equation model with mating inhomogeneity to discuss mosquito population suppression based on Wolbachia. Our analyses show that the wild mosquitoes could be eliminated if either the adult mortality rate exceeds the threshold [Formula: see text] or the release amount exceeds the threshold [Formula: see text] uniformly. We also present the nonlinear dependence of [Formula: see text] and [Formula: see text] on the parameters, respectively, as well as the effect of pesticide spraying on wild mosquitoes. Our simulations suggest that the releasing should be started at least 5 weeks before the peak dengue season, taking into account both the release amount and the suppression speed.

Wolbachia infection enhancing and decaying domains in mosquito population based on discrete models

In this article, we formulate and study a discrete equation model depicting the pattern of Wolbachia infection in a mosquito population. A domain in [Formula: see text] is called a Wolbachia infection enhancing (or decaying) domain if in which the Wolbachia infection frequency of the next generation is always bigger (or smaller) than that of the current generation. We first give a complete analysis of the equivalent Wolbachia infection frequency curves. And then we clearly characterize the Wolbachia infection enhancing domain and decaying domain for all of the parameters, respectively. Finally, some numerical examples are also provided to illustrate our theoretical results.