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The sterile insect technique controls mosquito-borne diseases such as malaria, dengue, and yellow fever through either eradication or depressing the associated vector population. We formulate a three-dimensional delayed mosquito population…
Mosquito-borne diseases cause several hundred thousand deaths every year. Deciphering mosquito host-seeking behavior is essential to prevent disease transmission through mosquito capture and surveillance. Despite recent substantial…
Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past years for fighting vector-borne diseases such as dengue, chikungunya and zika. Several strains of this bacterium cause cytoplasmic incompatibility…
The sterile insect technique has emerged recently as a biologically secure and effective tool for suppressing wild mosquito pests. To improve the performance of this strategy, understanding the interaction between wild and sterile…
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show…
The human body consists of microbiomes associated with the development and prevention of several diseases. These microbial organisms form several complex interactions that are informative to the scientific community for explaining disease…
Mosquitoes are vectors of viral diseases with epidemic potential in many regions of the world, and in absence of vaccines or therapies, their control is the main alternative. Chemical control through insecticides has been one of the…
This paper proposes two realistic and biologically viable methods for Wolbachia-based biocontrol of Aedes aegypti mosquitoes, assuming imperfect maternal transmission of the Wolbachia bacterium, incomplete cytoplasmic incompatibility, and…
We present a two-species population model in a well-mixed environment where the dynamics involves, in addition to birth and death, changes due to environmental factors and inter-species interactions. The novel dynamical components are…
Extensive efforts have been devoted to characterizing the rich connectivity patterns among the nodes (components) of such complex networks (systems), and in the course of development of research in this area, people have been prompted to…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
This work is devoted to the mathematical study of an optimization problem regarding control strategies of mosquito population in a heterogeneous environment. Mosquitoes are well-known vectors of diseases. For some diseases, such as dengue,…
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito…
The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of…
A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously…