Related papers: Mathematical modelling and simulation of HIV dynam…
This study develops and analyzes a stochastic differential equation (SDE) model for the dynamics of hepatitis B virus (HBV) infection. While deterministic frameworks have yielded important insights into viral behavior, they cannot…
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…
Although combination antiretroviral therapy (ART) is highly effective in suppressing viral load for people with HIV (PWH), many ART agents may exacerbate central nervous system (CNS)-related adverse effects including depression. Therefore,…
In this paper we study a model of HCV with mitotic proliferation, a saturation infection rate and a discrete intracellular delay: the delay corresponds to the time between infection of a infected target hepatocytes and production of new HCV…
In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a 'latent period' and 'the time for immune response' as delay parameters,…
We report a first in modeling and simulation of the effects of the HIV proteins on the (caspase dependent) apoptotic pathway in infected cells. This work is novel and is an extension on the recent reports and clarifications on the FAS…
HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. In this study, we propose a mathematical model…
In this paper, we propose an original complex network model for an epidemic problem in an heterogeneous geographical area. The complex network is constructed by coupling nonidentical instances of a HIV/AIDS epidemiological model for which a…
An important problem in contemporary immunology studies based on single-cell protein expression data is to determine whether cellular expressions are remodeled post infection by a pathogen. One natural approach for detecting such changes is…
We discuss methods for {\em a priori} selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an…
The primary goal of public health efforts to control HIV epidemics is to diagnose and treat people with HIV infection as soon as possible after seroconversion. The timing of initiation of antiretroviral therapy (ART) treatment after HIV…
We analyze 14,651 HIV1 reverse transcriptase (HIV RT) sequences from the Stanford HIV Drug Resistance Database labeled with treatment regimen in order to study the evolution this enzyme under drug selection in the clinic. Our goal is to…
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 continue our study of a model for cancer treatment, constructed in Dutta et. al., 2025, by adding Virotherapy to the Chemotherapy and Immunotherapy studied there. It is a dynamical system model for the spread of cancer in healthy tissue.…
In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses. The existence of traveling waves for the proposed model is established through the application of the celebrated Gersgorin…
Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…
Intrapatient HIV-1 evolution is dominated by selection on the protein level in the arms race with the adaptive immune system. When cytotoxic CD8+ T-cells or neutralizing antibodies target a new epitope, the virus often escapes via…
Existing strategies for determining the optimal treatment or monitoring strategy typically assume unlimited access to resources. However, when a health system has resource constraints, such as limited funds, access to medication, or…
Like many chronic diseases, human immunodeficiency virus (HIV) is managed over time at regular clinic visits. At each visit, patient features are assessed, treatments are prescribed, and a subsequent visit is scheduled. There is a need for…
When highly active antiretroviral therapy is administered for long periods of time to HIV-1 infected patients, most patients achieve viral loads that are ``undetectable'' by standard assay (i.e., HIV-1 RNA $ < 50$ copies/ml). Yet despite…