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In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always…
The role of direct cell-to-cell spread in viral infections - where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment - has come to be understood as essential to the dynamics…
A delayed model describing the dynamics of HIV (Human Immunodeficiency Virus) with CTL (Cytotoxic T Lymphocytes) immune response is investigated. The model includes four nonlinear differential equations describing the evolution of…
We propose and investigate a delayed model that studies the relationship between HIV and the immune system during the natural course of infection and in the context of antiviral treatment regimes. Sufficient criteria for local asymptotic…
In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates (rates…
The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have…
Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent…
We propose a time-parameterized analogy between the thermodynamic behavior of a 3-level energy system and the progression of the HIV infection described by the cell population evolution generated by an appropriated cellular automata model.…
We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of…
This paper explores a number of questions regarding optimal strategies evolved by viruses upon entry into a vertebrate host. The infected cell life cycle consists of a non-productively infected stage in which it is producing virions but not…
The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of…
We consider the standard three-component differential equation model for the growth of an HIV virion population in an infected host in the absence of drug therapy. The dynamical properties of the model are determined by the set of values of…
There has been interest in the interactions between infectious disease dynamics and behaviour for most of the history of mathematical epidemiology. This has included consideration of which mathematical models best capture each phenomenon,…
Hepatitis B virus is a global health threat, and its elimination by 2030 has been prioritised by the World Health Organisation. Here we present an age-structured model for the immune response to an HBV infection, which takes into account…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
Hepatitis type B is one of the most common infectious disease worldwide that can pose severe threats to human health up to the point that may contribute to severe liver damage or cancer. Over the past two decades a large number of dynamic…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about…
We analyze a within-host model of virus infection with antibody and CD8+ cytotoxic T lymphocyte (CTL) responses proposed by Schwartz et al. (2013). The goal of this work is to gain an overview of the stability of the biologically-relevant…
The use of oncolytic viruses as cancer treatment has received considerable attention in recent years, however the spatial dynamics of this viral infection is still poorly understood. We present here a stochastic agent-based model describing…