Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations

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.

Biological comparative study between Wolbachia-infected Aedes aegypti mosquito and Wolbachia-uninfected strain, Jeddah city, Saudi Arabia

In this study, samples of Wolbachia-infected Aedes aegypti mosquitoes were collected from Al-Safa district in Jeddah city, Saudi Arabia. The presence of Wolbachia bacteria in mosquitoes was confirmed by PCR technique and they were reared and propagated in the laboratory. Comparative studies were conducted between Wolbachia-infected A. Aegypti and the Wolbachia-uninfected laboratory strain in terms of their ability to withstand drought, resist two types of insecticides and the activities of pesticide detoxification enzymes. The Wolbachia-infected A. aegypti strain proved less able to withstand the drought period, as the egg-hatching rate of the Wolbachia-uninfected strain was greater than that of the Wolbachia-infected strain after one, two and three months of dry periods. Compared to the Wolbachia-uninfected strain, the Wolbachia-infected strain demonstrated a relatively greater resistance to tested pesticides, namely Baton 100EC and Fendure 25EC which may be attributed to the higher levels of the detoxification enzymes glutathione-S-transferase and catalase and the lower levels of esterase and acetylcholine esterase.

Discrete dynamical models on Wolbachia infection frequency in mosquito populations with biased release ratios

We develop two discrete models to study how supplemental releases affect the Wolbachia spreading dynamics in cage mosquito populations. The first model focuses on the case when only infected males are released at each generation. This release strategy has been proved to be capable of speeding up the Wolbachia persistence by suppressing the compatible matings between uninfected individuals. The second model targets the case when only infected females are released at each generation. For both models, detailed model formulation, enumeration of the positive equilibria and their stability analysis are provided. Theoretical results show that the two models can generate bistable dynamics when there are three positive equilibrium points, semi-stable dynamics for the case of two positive equilibrium points. And when the positive equilibrium point is unique, it is globally asymptotically stable. Some numerical simulations are offered to get helpful implications on the design of the release strategy.

Existence and stability of two periodic solutions for an interactive wild and sterile mosquitoes model

In this paper, we study the periodic and stable dynamics of an interactive wild and sterile mosquito population model with density-dependent survival probability. We find a release amount upper bound G∗, depending on the release waiting period T, such that the model has exactly two periodic solutions, with one stable and another unstable, provided that the release amount does not exceed G∗. A numerical example is also given to illustrate our results.

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.

Mosquito Control Based on Pesticides and Endosymbiotic Bacterium Wolbachia

Mosquito-borne diseases, such as dengue fever and Zika, have posed a serious threat to human health around the world. Controlling vector mosquitoes is an effective method to prevent these diseases. Spraying pesticides has been the main approach of reducing mosquito population, but it is not a sustainable solution due to the growing insecticide resistance. One promising complementary method is the release of Wolbachia-infected mosquitoes into wild mosquito populations, which has been proven to be a novel and environment-friendly way for mosquito control. In this paper, we incorporate consideration of releasing infected sterile mosquitoes and spraying pesticides to aim to reduce wild mosquito populations based on the population replacement model. We present the estimations for the number of wild mosquitoes or infection density in a normal environment and then discuss how to offset the effect of the heatwave, which can cause infected mosquitoes to lose Wolbachia infection. Finally, we give the waiting time to suppress wild mosquito population to a given threshold size by numerical simulations.

A Wolbachia infection model with free boundary

Scientists have been seeking ways to use Wolbachia to eliminate the mosquitoes that spread human diseases. Could Wolbachia be the determining factor in controlling the mosquito-borne infectious diseases? To answer this question mathematically, we develop a reaction-diffusion model with free boundary in a one-dimensional environment. We divide the female mosquito population into two groups: one is the uninfected mosquito population that grows in the whole region while the other is the mosquito population infected with Wolbachia that occupies a finite small region. The mosquito population infected with Wolbachia invades the environment with a spreading front governed by a free boundary satisfying the well-known one-phase Stefan condition. For the resulting free boundary problem, we establish criteria under which spreading and vanishing occur. Our results provide useful insights on designing a feasible mosquito releasing strategy that infects the whole mosquito population with Wolbachia and eradicates the mosquito-borne diseases eventually.

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].

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 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.

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.

Two-By-One model of cytoplasmic incompatibility: Synthetic recapitulation by transgenic expression of cifA and cifB in Drosophila

Wolbachia are maternally inherited bacteria that infect arthropod species worldwide and are deployed in vector control to curb arboviral spread using cytoplasmic incompatibility (CI). CI kills embryos when an infected male mates with an uninfected female, but the lethality is rescued if the female and her embryos are likewise infected. Two phage WO genes, cifA_wMel and cifB_wMel from the wMel Wolbachia deployed in vector control, transgenically recapitulate variably penetrant CI, and one of the same genes, cifA_wMel, rescues wild type CI. The proposed Two-by-One genetic model predicts that CI and rescue can be recapitulated by transgenic expression alone and that dual cifA_wMeland cifB_wMel expression can recapitulate strong CI. Here, we use hatch rate and gene expression analyses in transgenic Drosophila melanogaster to demonstrate that CI and rescue can be synthetically recapitulated in full, and strong, transgenic CI comparable to wild type CI is achievable. These data explicitly validate the Two-by-One model in wMel-infected D. melanogaster, establish a robust system for transgenic studies of CI in a model system, and represent the first case of completely engineering male and female animal reproduction to depend upon bacteriophage gene products.

Releases of Wolbachia-infected mosquitos are underway worldwide because Wolbachia block replication of Zika and Dengue viruses and spread themselves maternally through arthropod populations via cytoplasmic incompatibility (CI). The CI drive system depends on a Wolbachia-induced sperm modification that results in embryonic lethality when an infected male mates with an uninfected female, but this lethality is rescued when the female and her embryos are likewise infected. We recently reported that the phage WO genes, cifA and cifB, cause the sperm modification and cifA rescues the embryonic lethality caused by the wMel Wolbachia strain deployed in vector control. These reports motivated proposal of the Two-by-One model of CI whereby two genes cause lethality and one gene rescues it. Here we provide unequivocal support for the model in the Wolbachia strain used in vector control via synthetic methods that recapitulate CI and rescue in the absence of a Wolbachia infections. Our results reveal the set of phage WO genes responsible for this powerful genetic drive system, act as a proof-of-concept that these genes alone can induce gene drive like crossing patterns, and establish methodologies and hypotheses for future studies of CI in Drosophila. We discuss the implications of the Two-by-One model towards functional mechanisms of CI, the emergence of incompatibility between Wolbachia strains, vector control applications, and CI gene nomenclature.

Characterization of Wolbachia enhancing domain in mosquitoes with imperfect maternal transmission

A novel method to reduce the burden of dengue is to seed wild mosquitoes with Wolbachia-infected mosquitoes in dengue-endemic areas. Concerns in current mathematical models are to locate the Wolbachia introduction threshold. Our recent findings manifest that the threshold is highly dependent on the initial population size once Wolbachia infection alters the logistic control death rate of infected females. However, counting mosquitoes is beyond the realms of possibility. A plausible method is to monitor the infection frequency. We propose the concept of Wolbachia enhancing domain in which the infection frequency keeps increasing. A detailed description of the domain is presented. Our results suggest that both the initial population size and the infection frequency should be taken into account for optimal release strategies. Both Wolbachia fixation and extinction permit the oscillation of the infection frequency.