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 …

We review the general problem of random searches in the context of biological encounters.
We analyze deterministic and stochastic aspects of searching in general and address the …

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

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 …

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 …

We are concerned with a reaction–diffusion–advection SIS epidemic model with mass action
infection mechanism in a one dimensional bounded domain. We first prove the existence of …

We study the traveling waves of reaction-diffusion equations for a diffusive SIR model. The
existence of traveling waves is determined by the basic reproduction number of the …