Related papers: Analysis of a Stochastic Predator-Prey Model with …
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric…
How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments…
We consider the basic model of virus dynamics in the modeling of Human Immunodeficiency Virus (HIV), in a 2D heterogenous environment. It consists of two ODEs for the non-infected and infected $CD_4^+$ $T$ lymphocytes, $T$ and $I$, and a…
HIV-1 affects tens of millions of people worldwide. Current treatments often involve a cocktail of antiretroviral drugs, which are effective in reducing the virus and extending life spans. However, there is currently no FDA-approved HIV-1…
We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A…
We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a…
In this paper, the dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
We analyze 14,651 HIV1 reverse transcriptase (HIV RT) sequences from the Stanford HIV Drug Resistance Database labeled with treatment regimen in order to study the evolution this enzyme under drug selection in the clinic. Our goal is to…
This study utilizes mathematical models to assess progress toward achieving the UNAIDS 90-90-90 and 95-95-95 targets aimed at managing and eradicating HIV/AIDS. It contrasts stochastic and deterministic models, focusing on their utility in…
Like many chronic diseases, human immunodeficiency virus (HIV) is managed over time at regular clinic visits. At each visit, patient features are assessed, treatments are prescribed, and a subsequent visit is scheduled. There is a need for…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
An increasing number of control techniques are introduced to HIV infection problem to explore the options of helping clinical testing, optimizing drug treatments and to study the drug resistance situations. In such cases, complete/accurate…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature…
The process of infection of a host is complex, influenced by factors such as microbial variation within and between hosts as well as differences in dose across hosts. This study uses dose-response and within-host microbial infection models…
Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis…