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The search to understand how the HIV virus spreads inside the human body and how the immune response works to control it has motivated studies related to Mathematical Immunology. Actually, researches include the idea of mathematical models…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
Up to now, the effects of having heterogeneous networks of contacts have been studied mostly for diseases which are not persistent in time, i.e., for diseases where the infectious period can be considered very small compared to the lifetime…
We propose a fractional order model for HIV/AIDS transmission. Local and uniform stability of the fractional order model is studied. The theoretical results are illustrated through numerical simulations.
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is…
Bipartite networks are composed of two types of nodes and there are no links between nodes of the same type. Thus the study of epidemic spread and control on such networks is relevant to sexually transmitted diseases (STDs). When entire…
The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the…
The Devil Facial Tumour Disease (DFTD), a unique case of a transmissible cancer, had a devastating effect on its host, the Tasmanian Devil. Current estimates of its density are at roughly 20% of the pre-disease state, and single-population…
People living with HIV on antiretroviral therapy often have undetectable virus levels by standard assays, but "latent" HIV still persists in viral reservoirs. Eliminating these reservoirs is the goal of HIV cure research. The quantitative…
In this article, we propose a network spread model for HIV epidemics, wherein each individual is represented by a node of the transmission network and the edges are the connections between individuals along which the infection may spread.…
Parasite quiescence is the ability for the pathogen to be inactive, with respect to metabolism and infectiousness, for some amount of time and then become active (infectious) again. The population is thus composed of an inactive proportion,…
HIV increases the likelihood that a person will develop TB. Starting them on anti-retroviral therapy (ART) reduces their risk of TB but not to the level in HIV negative people. Since HIV-positive people who are on ART can expect to live a…
Multiple mechanisms in the HIV lifecycle play a role in its ability to evade therapy and become a chronic, difficult-to-treat infection. Within its major cellular target, the activated T cell, many steps occur between viral entry and viral…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior -- quantifying how contact…
In this work we develop a stochastic model of acute HIV infection, based on the well-known standard model, that allows us to simulate the complex mutation pathways of HIV escape from multiple CTL responses. Under this model, we describe two…
We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not…
The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We…
Recent clinical studies have shown that HIV disease pathogenesis can depend strongly on many factors at the time of transmission, including the strength of the initial viral load and the local availability of CD4+ T-cells. In this article,…