Simple paratransgenic mosquitoes models and their dynamics

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.

Overview of paratransgenesis as a strategy to control pathogen transmission by insect vectors

This article presents an overview of paratransgenesis as a strategy to control pathogen transmission by insect vectors. It first briefly summarises some of the disease-causing pathogens vectored by insects and emphasises the need for innovative control methods to counter the threat of resistance by both the vector insect to pesticides and the pathogens to therapeutic drugs. Subsequently, the state of art of paratransgenesis is described, which is a particularly ingenious method currently under development in many important vector insects that could provide an additional powerful tool for use in integrated pest control programmes. The requirements and recent advances of the paratransgenesis technique are detailed and an overview is given of the microorganisms selected for genetic modification, the effector molecules to be expressed and the environmental spread of the transgenic bacteria into wild insect populations. The results of experimental models of paratransgenesis developed with triatomines, mosquitoes, sandflies and tsetse flies are analysed. Finally, the regulatory and safety rules to be satisfied for the successful environmental release of the genetically engineered organisms produced in paratransgenesis are considered.

Periodic Orbits of a Mosquito Suppression Model Based on Sterile Mosquitoes

In this work, we investigate the existence and stability of periodic orbits of a mosquito population suppression model based on sterile mosquitoes. The model switches between two sub-equations as the actual number of sterile mosquitoes in the wild is assumed to take two constant values alternately. Employing the Poincaré map method, we show that the model has at most two T-periodic solutions when the release amount is not sufficient to eradicate the wild mosquitoes, and then obtain some sufficient conditions for the model to admit a unique or exactly two T-periodic solutions. In particular, we observe that the model displays bistability when it admits exactly two T-periodic solutions: the origin and the larger periodic solution are asymptotically stable, and the smaller periodic solution is unstable. Finally, we give two numerical examples to support our lemmas and theorems.

Culturable bacteria associated with Anopheles darlingi and their paratransgenesis potential

Background

Malaria remains a major public health problem in South America, mostly in the Amazon region. Among newly proposed ways of controlling malaria transmission to humans, paratransgenesis is a promising alternative. Paratransgenesis aims to inhibit the development of parasites within the vector through the action of genetically modified bacteria. The first step towards successful paratransgenesis in the Amazon is the identification of Anopheles darlingi symbiotic bacteria, which are transmitted vertically among mosquitoes, and are not pathogenic to humans.

Methods

Culturable bacteria associated with An. darlingi and their breeding sites were isolated by conventional microbiological techniques. Isolated strains were transformed with a GFP expressing plasmid, pSPT-1-GFP, and reintroduced in mosquitoes by feeding. Their survival and persistence in the next generation was assessed by the isolation of fluorescent bacteria from eggs, larvae, pupae and adult homogenates.

Results

A total of 179 bacterial strains were isolated from samples from two locations, Coari and Manaus. The predominant genera identified in this study were Acinetobacter, Enterobacter, Klebsiella, Serratia, Bacillus, Elizabethkingia, Stenotrophomonas and Pantoea. Two isolated strains, Serratia-Adu40 and Pantoea-Ovo3, were successfully transformed with the pSPT-1-GFP plasmid and expressed GFP. The fluorescent bacteria fed to adult females were transferred to their eggs, which persisted in larvae and throughout metamorphosis, and were detected in adult mosquitoes of the next generation.

Conclusion

Serratia-Adu40 and Pantoea-Ovo3 are promising candidates for paratransgenesis in An. darlingi. Further research is needed to determine if these bacteria are vertically transferred in nature.

Impulsive releases of sterile mosquitoes and interactive dynamics with time delay

To investigate the impact of periodic and impulsive releases of sterile mosquitoes on the interactive dynamics between wild and sterile mosquitoes, we adapt the new idea where only those sexually active sterile mosquitoes are included in the modelling process and formulate new models with time delay. We consider different release strategies and compare their model dynamics. Under certain conditions, we derive corresponding model formulations and prove the existence of periodic solutions for some of those models. We provide numerical examples to demonstrate the dynamical complexity of the models and propose further studies.

Modeling and control of mosquito-borne diseases with Wolbachia and insecticides

Mosquitoes cause more human suffering than any other organism. It is estimated that over one million people worldwide die from mosquito-borne diseases every year. With the continuous efforts of many researchers, Wolbachia gets more and more attention due to its characteristics of maternal transmission in mosquito population and it may cause cytoplasmic incompatibility (CI) which makes healthy females cannot fertilize normally after mating with infected males. In this paper, mathematical models are established to study Wolbachia transmission in mosquito population, and integrated mosquito control strategies are explored. Firstly, a classical ordinary differential system with general birth and death rate functions is established to describe the maternal transmission and CI effect. It is shown that the replacement strategy that the Wolbachia-uninfected mosquitoes are replaced by the infected ones is determined by the initial infection frequency. And Wolbachia spreads more easily for greater maternal transmission and CI rate. Moreover, all the wild mosquitoes will eventually be infected with Wolbachia if the maternal transmission is complete. Secondly, an impulsive state feedback control model is constructed to describe the integrated mosquito control. Besides Wolbachia, insecticides are sprayed when the quantity of mosquitoes reaches some Economic Threshold. The existence and stability of Wolbachia replacement periodic solution are discussed. Finally, some discussions are done and the future research directions are prospected.

Dynamics of interactive wild and sterile mosquitoes with time delay

We develop a delay differential equation model for the interactive wild and sterile mosquitoes. Different from the existing modelling studies, we assume that only those sexually active sterile mosquitoes play a role for the interactive dynamics. We consider the cases where the release amount is either constant or described by a given function of time. For the constant releases, we establish a threshold of releases to determine whether the wild mosquito suppression succeeds or fails. We study the existence and stability of the model equilibria. When the releases are described by given functions, the trivial equilibrium is no longer globally but locally uniformly asymptotically stable if the amount of releases is below the threshold whereas it is still globally uniformly asymptotically stable if the release amount is above the threshold. Numerical examples demonstrating the model dynamical features and brief discussions of our findings are also provided.