Wolbachia Dynamics in Mosquitoes with Incomplete CI and Imperfect Maternal Transmission by a DDE System

Wolbachia Invasion in Mosquitoes with Incomplete CI, Imperfect Maternal Transmission and Maturation Delay

The mechanism of cytoplasmic incompatibility (CI) is important in the study of Wolbachia invasion in wild mosquitoes. Su et al. (Bull Math Biol 84(9):95, 2022) proposed a delay differential equation model by relating the CI effect to maturation delay. In this paper, we investigate the dynamics of this model by allowing the same density-dependent death rate and distinct density-independent death rates. Through analyzing the existence and stability of equilibria, we obtain the parameter conditions for Wolbachia successful invasion if the maternal transmission is perfect. While if the maternal transmission is imperfect, we give the ranges of parameters to ensure failure invasion, successful invasion and partially suppressing, respectively. Meanwhile, numerical simulations indicate that the system may exhibit monostable and bistable dynamics when parameters vary. Particularly, in the bistable situation an unstable separatrix, like a line, exists when choosing constant functions as initial values; and the maturation delay affects this separatrix in an interesting way.

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.

A Fractional-Order Density-Dependent Mathematical Model to Find the Better Strain of Wolbachia

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.

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.