Yicang Zhou

Stability of periodic solutions for an SIS model with pulse vaccination

Pulse vaccination is an important strategy for the elimination of infectious diseases. A mathematical SIS model with pulse vaccination is formulated in this paper. The dynamical behavior of the model is studied, and the basic reproductive number R0 is defined. It is proved that the disease-free periodic solution is stable if R0 1. The global stability of the disease-free periodic solution is studied and sufficient condition is obtained. The existence and stability of the endemic periodic solution are investigated analytically and numerically.

Oscillatory viral dynamics in a delayed HIV pathogenesis model

We consider an HIV pathogenesis model incorporating antiretroviral therapy and HIV replication time. We investigate the existence and stability of equilibria, as well as Hopf bifurcations to sustained oscillations when drug efficacy is less than 100%. We derive sufficient conditions for the global asymptotic stability of the uninfected steady state. We show that time delay has no effect on the local asymptotic stability of the uninfected steady state, but can destabilize the infected steady state, leading to a Hopf bifurcation to periodic solutions in the realistic parameter ranges.

Modeling and dynamics of infectious diseases

A Brief Introduction of Some Results on Epidemiology Obtained by the Research Group in XJTU (Z Ma) Modeling SARS, West Nile Virus, Pandemic Influenza and Other Emerging Infectious Diseases: A Canadian Teams Adventure (F Brauer & J Wu) Diseases in Metapopulations (J Arino) Modeling the Start of a Disease Outbreak (F Brauer) Mathematical Techniques in the Evolutionary Epidemiology of Infectious Diseases (T Day) The Uses of Epidemiological Models in the Study of Disease Control (Z Feng et al.) Assessing the Burden of Congenital Rubella Syndrome and Ensuring Optimal Mitigation via Mathematical Modeling (J W Glasser & M Birmingham) Persistence of Vertically Transmitted Parasite Strains Which Protect Against More Virulent Horizontally Transmitted Strains (T Dhirasakdanon & H R Thieme) Richards Model: A Simple Procedure for Real-Time Prediction of Outbreak Severity (Y-H Hsieh) The Basic Reproduction Number and the Final Size of an Epidemic (J Watmough) Epidemic Models with Reservoirs (K P Hadeler) Global Stability in Multigroup Epidemic Models (H Guo et al.) Epidemic Models with Time Delays (W Wang) A Simulation Approach to Analysis of Antiviral Stockpile Sizes for Infuenza Pandemic (S Zhang) Modeling and Simulation Studies of West Nile Virus in Southern Ontario, Canada (H Zhu).

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 discrete epidemic model for SARS transmission and control in China

n Abstractn n Severe acute respiratory syndrome (SARS) is a rapidly spreading infectious disease which was transmitted in late 2002 and early 2003 to more than 28 countries through the medium of international travel. The evolution and spread of SARS has resulted in an international effort coordinated by the World Health Organization (WHO).n We have formulated a discrete mathematical model to investigate the transmission of SARS and determined the basic reproductive number for this model to use as a threshold to determine the asymptotic behavior of the model. The dependence of the basic reproductive number on epidemic parameters has been studied. The parameters of the model have been estimated on the basis of statistical data and numerical simulations have been carried out to describe the transmission process for SARS in China. The simulation results matches the statistical data well and indicate that early quarantine and a high quarantine rate are crucial to the control of SARS.n n

Community-based measures for mitigating the 2009 H1N1 pandemic in China.

Since the emergence of influenza A/H1N1 pandemic virus in March–April 2009, very stringent interventions including Fengxiao were implemented to prevent importation of infected cases and decelerate the disease spread in mainland China. The extent to which these measures have been effective remains elusive. We sought to investigate the effectiveness of Fengxiao that may inform policy decisions on improving community-based interventions for management of on-going outbreaks in China, in particular during the Spring Festival in mid-February 2010 when nationwide traveling will be substantially increased. We obtained data on initial laboratory-confirmed cases of H1N1 in the province of Shaanxi and used Markov-chain Monte-Carlo (MCMC) simulations to estimate the reproduction number. Given the estimates for the exposed and infectious periods of the novel H1N1 virus, we estimated a mean reproduction number of 1.68 (95% CI 1.45–1.92) and other A/H1N1 epidemiological parameters. Our results based on a spatially stratified population dynamical model show that the early implementation of Fengxiao can delay the epidemic peak significantly and prevent the disease spread to the general population but may also, if not implemented appropriately, cause more severe outbreak within universities/colleges, while late implementation of Fengxiao can achieve nothing more than no implementation. Strengthening local control strategies (quarantine and hygiene precaution) is much more effective in mitigating outbreaks and inhibiting the successive waves than implementing Fengxiao. Either strong mobility or high transport-related transmission rate during the Spring Festival holiday will not reverse the ongoing outbreak, but both will result in a large new wave. The findings suggest that Fengxiao and travel precautions should not be relaxed unless strict measures of quarantine, isolation, and hygiene precaution practices are put in place. Integration and prompt implementation of these interventions can significantly reduce the overall attack rate of pandemic outbreaks.

Projection of tuberculosis incidence with increasing immigration trends.

Tuberculosis (TB) incidence rates vary substantially from regions to regions and from countries to countries. In countries such as Canada where TB incidence rate is low, increasing immigration trends may have significant impact on the TB transmission patterns in these countries. In this study we formulate a deterministic epidemiological model of TB transmission in two demographically distinct populations: Canadian born and foreign born populations, in order to investigate the effects of this demographic distinction on the short-term incidence and long-term transmission dynamics, and with special emphasis on the impact of immigration latent TB cases on the overall TB incidence rate in the whole population.

Viral dynamics model with CTL immune response incorporating antiretroviral therapy

We present two HIV models that include the CTL immune response, antiretroviral therapy and a full logistic growth term for uninfected

Modelling disease spread in dispersal networks at two levels

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