Related papers: Towards Modeling HIV Long Term Behavior
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
We present a new joint longitudinal and survival model aimed at estimating the association between the risk of an event and the change in and history of a biomarker that is repeatedly measured over time. We use cubic B-splines models for…
Dynamic models have been successfully used in producing estimates of HIV epidemics at the national level due to their epidemiological nature and their ability to estimate prevalence, incidence, and mortality rates simultaneously. Recently,…
HIV is a deadly virus transmitted either through having of unprotected sex, mother to child transmission, sharing of unsterilized objects that is capable of making cut or wounds on the body, through blood or bodily fluid transmission. AIDS…
We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variable population size. Existence and uniqueness results for disease-free and endemic equilibrium points…
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…
We propose a stochastic SICA epidemic model for HIV transmission, described by stochastic ordinary differential equations, and discuss its perturbation by environmental white noise. Existence and uniqueness of the global positive solution…
HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models.…
The objective is to model longitudinal and survival data jointly taking into account the dependence between the two responses in a real HIV/AIDS dataset using a shared parameter approach inside a Bayesian framework. We propose a linear…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a…
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define "antigenicity", whether of the virus or of the adapted…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
As the global HIV pandemic enters its fourth decade, increasing numbers of surveillance sites have been established which allows countries to look into the epidemics at a finer scale, e.g. at sub-national levels. Currently, the epidemic…
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…
One of the cornerstones in combating the HIV pandemic is being able to assess the current state and evolution of local HIV epidemics. This remains a complex problem, as many HIV infected individuals remain unaware of their infection status,…
The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses such as HIV can cause chronic infections by evolving as quickly as the adaptive immune system, forming an…
Sexually transmitted diseases (STDs) are a group of pathogens infecting new hosts through sexual interactions. Due to its social and economic burden, multiple models have been proposed to study the spreading of pathogens. In parallel, in…
We consider a SICA model for HIV transmission on time scales. We prove permanence of solutions and we derive sufficient conditions for the existence and uniform asymptotic stability of a unique positive almost periodic solution of the…
Dynamic models have been successfully used in producing estimates of HIV epidemics at national level, due to their epidemiological nature and their ability to simultaneously estimate prevalence, incidence, and mortality rates. Recently, HIV…
The rates of escape and reversion in response to selection pressure arising from the host immune system, notably the cytotoxic T-lymphocyte (CTL) response, are key factors determining the evolution of HIV. Existing methods for estimating…