Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive number R0 is derived. It is proved that the dynamics of the model can be determined completely by the magnitude of R0. The infection-free equilibrium is globally asymptotically stable (unstable) if R01). There exists a chronic infection equilibrium and it is globally asymptotically stable if R0>1

The Global Stability Analysis for an SIS Model with Age and Infection Age Structures

27 pages, 1 article*The Global Stability Analysis for an SIS Model with Age and Infection Age Structures* (Zhou, Yicang; Song, Baojun; Ma, Zhien) 27 page

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

Discrete age-structured SEIT model with application to tuberculosis transmission in China

Age plays an important role in the transmission of some infectious diseases. A discrete SEIT model with age-structure is formulated and studied. The basic reproduction number, R0R0, of the model is defined. It is proved that R0=1R0=1 is a threshold to determine the disease extinction or persistence. The disease-free equilibrium is globally stable (unstable) if R01R0>1). There exists an endemic equilibrium, and the system is uniformly persistent if R0>1R0>1. The numerical simulation demonstrates that the endemic equilibrium may be globally asymptotically stable. The model is applied to describe tuberculosis (TB) transmission in China. The total number of the population, the incidence rate, the prevalent rate and its age structure match the statistical data well

The Bifurcation of Two Invariant Closed Curves in a Discrete Model

A discrete population model integrated using the forward Euler method is investigated. The qualitative bifurcation analysis indicates that the model exhibits rich dynamical behaviors including the existence of the equilibrium state, the flip bifurcation, the Neimark-Sacker bifurcation, and two invariant closed curves. The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory. Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves

Competitive Coexistence in a Two-Strain Epidemic Model with a Periodic Infection Rate

In this article, we study the global dynamical behavior of a two-strain SIS model with a periodic infection rate. The positivity and boundedness of solutions are established, and the competitive exclusion conditions are given for the model. The conditions for the global stability of the disease-free equilibrium and persistence of the model are obtained. The conditions of coexistence in this model are also found. Finally, the conditions of uniqueness of the solution are proved