A delay suppression model with sterile mosquitoes release period equal to wild larvae maturation period

Effectiveness evaluation of mosquito suppression strategies on dengue transmission under changing temperature and precipitation

Widespread resurgence of dengue outbreaks has seriously threatened the global health. Due to lack of treatments and vaccines, one key strategy in dengue control is to reduce the vector population size. As an environment-friendly mosquito control approach, releasing male mosquitoes transinfected with specific Wolbachia strain into the field to suppress the wild mosquito population size has become wildly accepted. The current study evaluates the effectiveness of this suppression strategy on dengue control under changing temperature and precipitation profiles. We formulate a mathematical model which includes larval intra-specific competition, the maturation period for mosquitoes, the extrinsic incubation period (EIP) and intrinsic incubation period (IIP). The persistence of mosquitoes and disease is discussed in terms of two basic reproduction numbers (RM and R0) and the release ratio pw. Further numerical simulations are carried out to not only validate theoretical results, but also provide interesting quantitative observations. Sensitivity analysis on the reproduction numbers, peak size, peak time and the final epidemic size is performed with respect to model parameters, which highlights effective control measures against dengue transmission. Moreover, by assuming temperature and precipitation dependent mosquito-related parameters, the model can be used to project the effectiveness of releasing Wolbachia-carrying males under climatic variations. It is shown that the effectiveness of various control strategies is highly dependent on the changing temperature and precipitation profiles. In particular, the model projects that it is most challenging to control the disease at the favorable temperature (around 27∼30∘C) and precipitation (5∼8mm/day) range, during which the basic reproduction number R0 is very high and more Wolbachia-infected males should be released.

Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay

Here, we formulated a delayed mosquito population suppression model including two switching sub-equations, in which we assumed that the growth of the wild mosquito population obeys the Ricker-type density-dependent survival function and the release period of sterile males equals the maturation period of wild mosquitoes. For the time-switched delay model, to tackle with the difficulties brought by the non-monotonicity of its growth term to its dynamical analysis, we employed an essential transformation, derived an auxiliary function and obtained some expected analytical results. Finally, we proved that under certain conditions, the number of periodic solutions and their global attractivities for the delay model mirror that of the corresponding delay-free model. The findings can boost a better understanding of the impact of the time delay on the creation/suppression of oscillations harbored by the mosquito population dynamics and enhance the success of real-world mosquito control programs.

Mathematical modelling and release thresholds of transgenic sterile mosquitoes

We formulate simple differential equation models to study the impact of releases of transgenic sterile mosquitoes carrying a dominant lethal on mosquito control based on the modified sterile insects technique. The early acting bisex, late acting bisex, early acting female-killing, and late acting female-killing lethality strategies are all considered. We determine release thresholds of the transgenic sterile mosquitoes, respectively, for these models by investigating the existence of positive equilibria and their stability. We compare the model dynamics, in particular, the thresholds of the models numerically. The late acting lethality strategies are generally more effective than their corresponding early acting lethality strategies, but the comparison between the late acting bisex and early acting female-killing lethality strategies depends on different parameter settings.

A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession

Releasing Wolbachia-infected male mosquitoes to suppress wild female mosquitoes through cytoplasmic incompatibility has shown great promise in controlling and preventing mosquito-borne diseases. To make the release logistically and economically feasible, we propose a saturated release strategy, which is only implemented during the epidemic season of mosquito-borne diseases. Under this assumption, the model becomes a seasonally switching ordinary differential equation model. The seasonal switch brings rich dynamics, including the existence of a unique periodic solution or exactly two periodic solutions, which are proved by using the qualitative property of the Poincaré map. Sufficient conditions are also obtained for determining the stability of the periodic solutions.

The phylogeny and distribution of Wolbachia in two pathogen vector insects, Asian citrus psyllid and Longan psyllid

Background

Wolbachia is the most abundant bacterial endosymbiont among insects. It can play a prominent role in the development, reproduction and immunity of its given insect host. To date, Wolbachia presence is well studied within aphids, whiteflies and planthoppers, but relatively few studies have investigated its presence in psyllids.

Methods

Here, the infection status of Wolbachia in five species of psyllid, including Asian citrus psyllid Diaphorina citri and longan psyllid Cornegenapsylla sinica was investigated. The phylogenetic relationships of different Wolbachia lines and their infection density and patterns in D. citri and C. sinica from different countries was also examined.

Results

The infection rates of Wolbachia in D. citri and C. sinica were both 100%, and their sequencing types are ST173 and ST532 respectively. Phylogenetic analysis revealed that the Wolbachia lines in D. citri and C. sinica both belong to the Con subgroup of Wolbachia supergroup B. In addition, Wolbachia displayed a scattered localization pattern in the 5th instar nymphs and in the reproductive organs of both D. citri and C. sinica but differed in other tissues; it was highest in the midgut, lowest in the salivary glands and medium in both the testes and ovaries.

Conclusion

Our findings assist in further understanding the coevolution of Wolbachia and its psyllid hosts. Given that Wolbachia could play an important role in insect pest control and pathogen transmission inhibition, our findings may also provide new insights for development of control strategies for D. citri and C. sinica.

Dynamics analysis of stage-structured wild and sterile mosquito interaction impulsive model

In this paper, we study a stage-structured wild and sterile mosquito interaction impulsive model. The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically. The existence of trivial periodic solutions is obtained, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem, respectively. And we prove the existence conditions of non-trivial periodic solutions and their local stability. We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions. All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range and even make them extinct. Finally, numerical simulation verifies our theoretical results.

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.

Dynamic Behavior of an Interactive Mosquito Model under Stochastic Interference

For decades, mosquito-borne diseases such as dengue fever and Zika have posed serious threats to human health. Diverse mosquito vector control strategies with different advantages have been proposed by the researchers to solve the problem. However, due to the extremely complex living environment of mosquitoes, environmental changes bring significant differences to the mortality of mosquitoes. This dynamic behavior requires stochastic differential equations to characterize the fate of mosquitoes, which has rarely been considered before. Therefore, in this article, we establish a stochastic interactive wild and sterile mosquito model by introducing the white noise to represent the interference of the environment on the survival of mosquitoes. After obtaining the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic system, we study the dynamic behavior of the stochastic model by constructing a series of suitable Lyapunov functions. Our results show that appropriate stochastic environmental fluctuations can effectively inhibit the reproduction of wild mosquitoes. Numerical simulations are provided to numerically verify our conclusions: the intensity of the white noise has an effect on the extinction and persistence of both wild and sterile mosquitoes.