Xiao-Qiang Zhao

Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction–diffusion models

Abstract The theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time-delayed reaction and diffusion population models.

A tuberculosis model with seasonality.

The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. A TB model incorporating seasonality is developed and the basic reproduction ratio R0 is defined. It is shown that the disease-free equilibrium is globally asymptotically stable and the disease eventually disappears if R0<1, and there exists at least one positive periodic solution and the disease is uniformly persistent if R0>1. Numerical simulations indicate that there may be a unique positive periodic solution which is globally asymptotically stable if R0>1. Parameter values of the model are estimated according to demographic and epidemiological data in China. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in China.

A Climate-Based Malaria Transmission Model with Structured Vector Population

In this paper, we present a malaria transmission model with periodic birth rate and age structure for the vector population. We first introduce the basic reproduction ratio for this model and then show that there exists at least one positive periodic state and that the disease persists when

A reaction–diffusion malaria model with incubation period in the vector population

\mathcal{R}_0>1

GLOBAL STABILITY OF MONOSTABLE TRAVELING WAVES FOR NONLOCAL TIME-DELAYED REACTION-DIFFUSION EQUATIONS ∗

. It is also shown that the disease will die out if

A reaction-diffusion SIS epidemic model in a time-periodic environment

\mathcal{R}_0<1

Monotone wavefronts of the nonlocal Fisher–KPP equation*

, provided that the invasion intensity is not strong. We further use these analytic results to study the malaria transmission cases in KwaZulu-Natal Province, South Africa. Some sensitivity analysis of

Bistable Traveling Waves for Monotone Semiflows with Applications

\mathcal{R}_0

Global attractivity in monotone and subhomogeneous almost periodic systems

is performed, and in particular, the potential impact of climate change on seasonal transmission and populations at risk of the disease is analyzed.

An Epidemic Model with Population Dispersal and Infection Period

Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period (EIP) of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction–diffusion model. We then define the basic reproduction ratio