相关论文: Spatial and non-spatial stochastic models for immu…
We consider a stochastic model for a pathogen population in the presence of an immune response, in which pathogen types are partially ordered by ancestry and the immune system must eliminate ancestor types before it can eliminate their…
We consider a spatial stochastic model for a pathogen population growing inside a host that attempts to eliminate the pathogens through its immune system. The pathogen population is divided into different types. A pathogen can either…
We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…
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 introduce and analyze a within-host dynamical model of the coevolution between rapidly mutating pathogens and the adaptive immune response. Pathogen mutation and a homeostatic constraint on lymphocytes both play a role in allowing the…
Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…
Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally…
Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space…
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…
We introduce a generalized version of the frog model to describe the invasion of a parasite population in a spatially structured immobile host population with host immunity on the integer line. Parasites move according to simple symmetric…
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…
Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health, regarding pathogen emergence, maintenance, and evolution. The full description of…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
Biological organisms have evolved a wide range of immune mechanisms to defend themselves against pathogens. Beyond molecular details, these mechanisms differ in how protection is acquired, processed and passed on to subsequent generations…
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
The immune system recognizes a myriad of invading pathogens and their toxic products. It does so with a finite repertoire of antibodies and T cell receptors. We here describe theories that quantify the immune system dynamics. We describe…
Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature…
Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality…
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…