Related papers: Mathematical modeling of antigenicity for HIV dyna…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
In this letter we study the full semi-conservative treatment of a model for the co-evolution of a virus and an adaptive immune system. Regions of viability are calculated for both conservatively and semi-conservatively replicating viruses…
Network models are increasingly used to study infectious disease spread. Exponential Random Graph models have a history in this area, with scalable inference methods now available. An alternative approach uses mechanistic network models.…
$\textbf{Background:}$ High mutability of HIV is the driving force of antiretroviral drug resistance, which represents a medical care challenge. $\textbf{Method and Model Equation:}$ To detect the mutability of each gene in the HIV-1…
With the launch of second line anti-retroviral therapy for HIV infected individuals, there has been an increased expectation on surviving period of people with HIV. We consider previously well-known models in HIV epidemiology where the…
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…
Antibiotic resistance is a growing public health problem. To gain a fundamental understanding of resistance evolution, a combination of systematic experimental and theoretical approaches is required. Evolution experiments combined with…
This chapter presents the main lines of agent based modeling in the field of medical research. The general diagram consists of a cohort of patients (virtual or real) whose evolution is observed by means of so-called evolution models.…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and…
We numerically study a dynamical system model of an idiotypic immune network with a small number of degrees of freedom. The model was originally introduced by Varela et.al., and describes antibodies interacting in a body in order to prepare…
We analyse a minimal model for the primary response in the adaptive immune system comprising three different players: antigens, T and B cells. We assume B-T interactions to be diluted and sampled locally from heterogeneous degree…
We propose a population model for HIV-TB co-infection dynamics by considering treatments for HIV infection, active tuberculosis and co-infection. The HIV only and TB only models are analyzed separately, as well as full model. The basic…
Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the…
Recognition of pathogens relies on families of proteins showing great diversity. Here we construct maximum entropy models of the sequence repertoire, building on recent experiments that provide a nearly exhaustive sampling of the IgM…
The immune response to a pathogen has two basic features. The first is the expansion of a few pathogen-specific cells to form a population large enough to control the pathogen. The second is the process of differentiation of cells from an…
The process of infection of a host is complex, influenced by factors such as microbial variation within and between hosts as well as differences in dose across hosts. This study uses dose-response and within-host microbial infection models…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…