Related papers: Two-dimensional stability analysis in a HIV model …
In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is…
In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular…
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout…
In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate…
We model the spontaneous assembly of a capsid (a virus's closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an…
In this work we have investigated the evolutionary dynamics of a generalist pathogen, e.g. a virus population, that evolves towards specialisation in an environment with multiple host types. We have particularly explored under which…
The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of many kinds of infectious diseases. In the study of mathematical models of infectious diseases it is…
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…
Polymorphism has been observed in viral capsid assembly, demonstrating the ability of identical protein dimers to adopt multiple geometries under the same solution conditions. A well-studied example is the hepatitis B virus (HBV), which…
HIV-1 can disseminate between susceptible cells by two mechanisms: cell-free infection following fluid-phase diffusion of virions and by highly-efficient direct cell-to-cell transmission at immune cell contacts. The contribution of this…
We propose a model for the human immunodeficiency virus type 1 (HIV-1) infection with intracellular delay and prove the local asymptotical stability of the equilibrium points. Then we introduce a control function representing the efficiency…
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of…
Broadly neutralizing antibodies are promising candidates for treatment and prevention of HIV-1 infections. Such antibodies can temporarily suppress viral load in infected individuals; however, the virus often rebounds by escape mutants that…
In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from…
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…
We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…
Reports from the Health Department in the Philippines show that cases of Human Immunodeficiency Virus (HIV) are increasing despite management and control efforts by the government. Worldwide, the Philippines has one of the fastest growing…
This paper deals with a simplified SIS model, which describes the transmission of the disease in time-periodic heterogeneous environment. To understand the impact of spatial heterogeneity of environment and small advection on the…
We propose a new mathematical model for the transmission dynamics of the human immunodeficiency virus (HIV). Global stability of the unique endemic equilibrium is proved. Then, based on data provided by the "Progress Report on the AIDS…