Wenzhang Huang
University of Alabama in Huntsville
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Featured researches published by Wenzhang Huang.
Siam Journal on Applied Mathematics | 1992
Wenzhang Huang; Kenneth L. Cooke; Carlos Castillo-Chavez
This paper examines a multigroup epidemic model with variable population size. It is shown that even in the case of proportionate mixing, multiple endemic equilibria are possible. The significance of these results in the study of the dynamics of sexually transmitted diseases and theoretical biology is discussed.
Journal of Dynamics and Differential Equations | 2001
Zhilan Feng; Wenzhang Huang; Carlos Castillo-Chavez
The qualitative behaviors of a system of ordinary differential equations and a system of differential-integral equations, which model the dynamics of disease transmission for tuberculosis (TB), have been studied. It has been shown that the dynamics of both models are governed by a reproductive number. All solutions converge to the origin (the disease-free equilibrium) when this reproductive number is less than or equal to the critical value one. The disease-free equilibrium is unstable and there exists a unique positive (endemic) equilibrium if the reproductive number exceeds one. Moreover, the positive equilibrium is stable. Our results show that the qualitative behaviors predicted by the model with arbitrarily distributed latent stage are similar to those given by the TB model with an exponentially distributed period of latency.
Siam Journal on Applied Mathematics | 1999
Carlos Castillo-Chavez; Wenzhang Huang; Jia Li
In this paper we give a rather complete analysis for a two-sex, susceptible-infective-susceptible (SIS) sexually transmitted disease (STD) model with two competing strains, where the females are divided into two different groups based on their susceptibility to two distinct pathogenic strains. We investigate the existence and stability of the boundary equilibria that characterize the competitive exclusion of the two competing strains; we also investigate the existence and stability of the positive coexistence equilibrium, which characterizes the possibility of coexistence of the two strains. We obtain sufficient and necessary conditions for the existence and global stability of these equilibria. We verify that there is a strong connection between the stability of the boundary equilibria and the existence of the coexistence equilibrium---that is, there exists a unique coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability. This coexistence is globally stable o...
Proceedings of the American Mathematical Society | 1996
Kenneth L. Cooke; Wenzhang Huang
The local stability of the equilibrium for a general class of statedependent delay equations of the form ẋ(t) = f ( xt, ∫ 0 −r0 dη(s)g(xt(−τ(xt) + s)) ) has been studied under natural and minimal hypotheses. In particular, it has been shown that generically the behavior of the state-dependent delay τ (except the value of τ) near an equilibrium has no effect on the stability, and that the local linearization method can be applied by treating the delay τ as a constant value at the equilibrium.
Mathematical and statistical approaches to AIDS epidemiology | 1990
Carlos Castillo-Chavez; Kenneth L. Cooke; Wenzhang Huang; Simon A. Levin
In this paper, we restate previously obtained results on homogeneously-mixed single-group models for HIV (human immunodeficiency virus) with distributed waiting times in the infectious class. We also present some simulations that illustrate the effects of a changing mean sexual activity in the dynamics of HIV, and formulate a single group model for a heterogeneously mixed population with continuously-distributed sexual activity. This model forms the basis for our formulation of an N-group model with arbitrary social/sexual mixing. The local stability analysis of this N-group model is discussed. A two-group example under preferred mixing that has multiple endemic equilibria is presented, as well as an example for an N-group model, under proportionate mixing, possessing multiple endemic equilibria.
Mathematical Biosciences and Engineering | 2010
Wenzhang Huang; Maoan Han; Kaiyu Liu
Recently an SIS epidemic reaction-diffusion model with Neumann (or no-flux) boundary condition has been proposed and studied by several authors to understand the dynamics of disease transmission in a spatially heterogeneous environment in which the individuals are subject to a random movement. Many important and interesting properties have been obtained: such as the role of diffusion coefficients in defining the reproductive number; the global stability of disease-free equilibrium; the existence and uniqueness of a positive endemic steady; global stability of endemic steady for some particular cases; and the asymptotical profiles of the endemic steady states as the diffusion coefficient for susceptible individuals is sufficiently small. In this research we will study two modified SIS diffusion models with the Dirichlet boundary condition that reflects a hostile environment in the boundary. The reproductive number is defined which plays an essential role in determining whether the disease will extinct or persist. We have showed that the disease will die out when the reproductive number is less than one and that the endemic equilibrium occurs when the reproductive number is exceeds one. Partial result on the global stability of the endemic equilibrium is also obtained.
Journal of Dynamics and Differential Equations | 2001
Wenzhang Huang
For a system of reaction–diffusion equations that models the interaction of n mutualist species, the existence of the bistable traveling wave solution has been proved where the nonlinear reaction terms possess a certain type of monotonicity. However the problem of whether there can be two distinct traveling waves remains open. In this paper we use a homotopy approach incorporated with the Liapunov–Schmidt method to show that the bistable traveling wave solution is unique. Our method developed in this paper can also be applied to study the existence and uniqueness of traveling wave solutions for some competition models.
Archive | 2002
Carlos Castillo-Chavez; Wenzhang Huang
The recruitment of new suceptibles into a core group of sexually-active individuals may depend on the current levels of infection within a population. We extend the formalism of Hadeler and Castillo-Chavez (1995), that includes prevalence dependent recruitment rates, to include age structure within core and noncore populations. Some mathematical results are stated but only a couple of proofs are included since our objetives are to highlight the modeling process and the dynamic possibilities. This paper concludes with an example where endemic distributions can be supported when the basic reproductive number R0 is less than one. Systems that are capable of supporting multiple attractors are more likely to support disease re-emergence. This model is likely to support stable multiple attractors when R0 < 1.
Siam Journal on Applied Mathematics | 2006
Kenneth L. Cooke; Richard H. Elderkin; Wenzhang Huang
This paper focuses on predator-prey models with juvenile/mature class structure for each of the predator and prey populations in turn, further classified by whether juvenile or mature individuals are active with respect to the predation process. These models include quite general prey recruitment at every stage of analysis, with mass action predation, linear predator mortality as well as delays in the dynamics due to maturation. As a base for comparison we briefly establish that the similar model without delays cannot support sustained oscillation, but it does have predator extinction or global approach to predator-prey coexistence depending on whether the ratio
Siam Journal on Applied Mathematics | 2012
Carlos Castillo-Chavez; Zhilan Feng; Wenzhang Huang
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