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Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit dengue virus. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to…
We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and…
We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a…
In this paper we study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of…
Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected…
According to the World Health Organization the global incidence rate of dengue infections have risen drastically in recent years. It is estimated that globally the number of new infections is in the range of $100$ to $400$ million per…
Wolbachia is a naturally occurring bacterium that can infect Aedes mosquitoes and reduce the transmission of mosquito-borne diseases, including dengue fever, Zika, and chikungunya. Field trials have been conducted worldwide to suppress…
In this paper, Wolbachia infection in a bisexual and diploid population with a fixed cytoplasmic incompatibility rate $w$ and maternal transmission rate $d$ is studied as an evolution algebra. As the cytoplasmic incompatibility (CI) of the…
Wolbachia, a maternally transmitted endosymbiont, offers a powerful biological control strategy for mosquito-borne diseases such as dengue, Zika, and malaria. We develop an integro-difference equation (IDE) model that integrates Wolbachia's…
Arboviral infections, especially dengue, continue to cause significant health burden in their endemic regions. One of the strategies to tackle these infections is to replace the main vector agent, Ae. aegypti, with the ones incapable of…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
Waning immunity and reinfection are critical features of many infectious diseases, but epidemiological models often fail to capture the intricate interaction between an individual's history of immunity and their current infection status;…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are…
Wolbachia are common endosymbionts of terrestrial arthropods, and are also found in nematodes: the animal-parasitic filaria, and the plant-parasite Radopholus similis. Lateral transfer of Wolbachia DNA to the host genome is common. We…
This is the first paper in the sequel studying the Wolbachia-infection in bisexual populations. This paper considers the behavior of the population as a discrete dynamical system. The recurrence relation is obtained as a function of the…
The release of Wolbachia-infected mosquitoes is a promising strategy for controlling Aedes aegypti populations, but exposure to high temperatures can induce temporary infection loss and compromise long-term persistence. In this work, we…
Dynamics of the infectious disease transmission is often best understood taking into account the structure of population with respect to specific features, in example age or immunity level. Practical utility of such models depends on the…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of…