Related papers: Dynamics of an Intra-host Diffusive Pathogen Infec…
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…
Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health with a yearly estimated global burden of 2.9 million cases. Although the majority of existing models for the…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
Discrete and Continuous Dynamics is the first in a series of articles on Network Models for Epidemiology. This project began in the Fall quarter of 2014 in my continuous modeling course. Since then, it has taken off and turned into a series…
Human pathogens transmitted through environmental pathways are subject to stress and pressures outside of the host. These pressures may cause pathogen pathovars to diverge in their environmental persistence and their infectivity on an…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis…
Besides mimicking bio-chemical and multi-scale communication mechanisms, molecular communication forms a theoretical framework for virus infection processes. Towards this goal, aerosol and droplet transmission has recently been modeled as a…
The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new…
We consider the dynamic infection spread model that is based on the discrete SIR model which assumes infections to be spread over time via infected and non-isolated individuals. In our system, the main objective is not to minimize the…
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…
A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and…
The analysis of diffusion processes in real-world propagation scenarios often involves estimating variables that are not directly observed. These hidden variables include parental relationships, the strengths of connections between nodes,…
Threshold-driven models and game theory are two fundamental paradigms for describing human interactions in social systems. However, in mimicking social contagion processes, models that simultaneously incorporate these two mechanisms have…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
Despite being similar in structure, functioning, and size viral pathogens enjoy very different mostly well-defined ways of life. They occupy their hosts for a few days (influenza), for a few weeks (measles), or even lifelong (HCV), which…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time of isolation (i.e. hospitalization) of infectious population is the main time-dependent…