Related papers: Mathematical model of immune response to hepatitis…
We study within-host HIV dynamics using a three--component nonlinear ordinary differential equation model for healthy CD4$^{+}$ T cells, infected CD4$^{+}$ T cells, and free virus. In addition to the baseline model without treatment, we…
This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive orthant is exhibited.…
We model the immune surveillance of a pathogen which passes through $n$ immunologically distinct stages. The biological parameters of this system induce a partial order on the stages, and this, in turn, determines which stages will be…
We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is…
This paper develops a second-order explicit predictor-corrector numerical approach for solving a mathematical model on the dynamic of cytokine expressions and human immune cell activation in response to the bacterium staphylococcus aureus…
We establish some properties of a within host mathematical model of malaria proposed by Recker et al which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria…
We develop a stochastic model to study the specific response of the immune system. The model is based on the dynamical interaction between Regulatory and Effector CD4+ T cells in the presence of Antigen Presenting Cells inside a lymphatic…
Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given data sets. This…
In vaccine development, the temporal profiles of relative abundance of subtypes of immune cells (T-cells) is key to understanding vaccine efficacy. Complex and expensive experimental studies generate very sparse time series data on this…
We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected…
Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes…
Mathematical oncology is a rapidly evolving interdisciplinary field that uses mathematical models to enhance our understanding of cancer dynamics, including tumor growth, metastasis, and treatment response. Tumor-immune interactions play a…
Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…
We present a dynamical model of lipoprotein metabolism derived by combining a cascading process in the blood stream and cellular level regulatory dynamics. We analyse the existence and stability of equilibria and show that this…
How does immune system evolve functional proteins - potent antibodies - in such a short time? We address this question using a microscopic, protein-level, sequence-based model of humoral immune response with explicitly defined interactions…
Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In…
Chronic critical illness (CCI) is a disease state in which, following an initial insult, a patient neither recovers nor dies but instead remains in a state of critical illness. CCI is characterized by prolonged organ dysfunction, weight…
A dynamic model of non-lineal time-dependent ordinary differential equations (ODE) has been applied to the interactions of a HIV infection with the immune system cells. This model has been simplified into two compartments: lymph node and…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
We study some simple mathematical models designed to test the following hypothesis: can a pathogen escape the immune system only because of its high probability of mutation? We propose both spatial and non-spatial models. In all of our…