This paper is an introductory review of the problem of front propagation into unstable states.
Our presentation is centered around the concept of the asymptotic linear spreading velocity …

Infectious diseases are a threat to human health and a hindrance to societal development.
Consequently, the spread of diseases in both time and space has been widely studied …

For epidemiologists, evolutionary biologists, and health-care professionals, real-time and
predictive modeling of infectious disease is of growing importance. This book provides a …

We examine a nonreciprocally coupled dynamical model of a mixture of two diffusing
species. We demonstrate that nonreciprocity, which is encoded in the model via antagonistic …

This book surveys significant modern contributions to the mathematical theories of
generalized heat wave equations. The first three chapters form a comprehensive survey of …

A brief introduction to the formulation of various types of stochastic epidemic models is
presented based on the well-known deterministic SIS and SIR epidemic models. Three …

In the present paper, we are concerned with a susceptible-infected-susceptible epidemic
reaction-diffusion model governed by a mass action infection mechanism and linear birth …

The theory of reaction–diffusion waves begins in the 1930s with the works in population
dynamics, combustion theory and chemical kinetics. At the present time, it is a well …

If we had to formulate in one sentence what this book is about, it might be “How partial
differential equations can help to understand heat explosion, tumor growth or evolution of …

The next generation matrix approach for calculating the basic reproduction number is
summarized for discrete-time epidemic models. This approach is applied to six disease …