Zhilan Feng

Global stability of an age-structure model for TB and its applications to optimal vaccination strategies

This article focuses on the study of an age-structure model for the disease transmission dynamics of tuberculosis in populations that are subjected to a vaccination program. We first show that the infection-free steady state is globally stable if the basic reproductive number R0 is below one, and that an endemic steady state exists when the reproductive number in the presence of vaccine is above one. We then apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategies can be either one- or two-age strategies.

MATHEMATICAL ANALYSIS OF AGE-STRUCTURED HIV-1 DYNAMICS WITH COMBINATION ANTIRETROVIRAL THERAPY*

Various classes of antiretroviral drugs are used to treat HIV infection, and they target different stages of the viral life cycle. Age-structured models can be employed to study the impact of these drugs on viral dynamics. We consider two models with age-of-infection and combination therapies involving reverse transcriptase, protease, and entry/fusion inhibitors. The reproductive number R is obtained, and a detailed stability analysis is provided for each model. Interestingly, we find in the age-structured model a different functional dependence of R onRT , the efficacy of a reverse transcriptase inhibitor, than that found previously in nonage-structured models, which has significant implications in predicting the effects of drug therapy. The influence of drug therapy on the within-host viral fitness and the possible development of drug-resistant strains are also discussed. Numerical simulations are performed to study the dynamical behavior of solutions of the models, and the effects of different combinations of antiretroviral drugs on viral dynamics are compared.

DYNAMICS OF TWO-STRAIN INFLUENZA WITH ISOLATION AND PARTIAL CROSS-IMMUNITY ∗

The time evolution of the influenza A virus is linked to a nonfixed landscape driven by interactions between hosts and competing influenza strains. Herd-immunity, cross-immunity, and age-structure are among the factors that have been shown to support strain coexistence and/or disease oscillations. In this study, we put two influenza strains under various levels of (interference) competition. We establish that cross-immunity and host isolation lead to periodic epidemic outbreaks (sustained oscillations) in this multistrain system. We compute the isolation reproductive number for each strain (

On the Role of Variable Latent Periods in Mathematical Models for Tuberculosis

\Re_i

A TWO-STRAIN TUBERCULOSIS MODEL WITH AGE OF INFECTION ∗

) independently, as well as for the full system (

Recurrent outbreaks of childhood diseases revisited: The impact of isolation

\Re_q

Emergence of drug resistance: implications for antiviral control of pandemic influenza.

), and show that when

Endemic models with arbitrarily distributed periods of infection I: Fundamental properties of the model

\Re_q < 1

Merging Spatial and Temporal Structure within a Metapopulation Model

, both strains die out. Subthreshold coexistence driven by cross-immunity is possible even when the isolation reproductive number of one strain is below 1. Conditions that guarantee a winning type or coexistence are established in general. Oscillatory coexistence is established via Hopf bifurcation theory and confirmed via n...

Transmission Dynamics of an Influenza Model with Vaccination and Antiviral Treatment

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.