JOINT MATHEMATICS COLLOQUIUMUNIVERSITY OF IDAHOWASHINGTON STATE UNIVERSITY |
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| This talk concerns the speaker's
collaborative work with Prof. Xueying Wang. Cholera is an infectious disease caused by the bacterium Vibrio cholerae. Its spread and consequence in countries of Africa, Southeast Asia, Haiti and central Mexico are well-known and indicates the need for an efficient mathematical model to control the spread of such a disease. In dynamics of population biology, an important disease threshold is called the basic reproduction number R0, which measures the expected number of secondary infections caused by one infectious individual during its infectious period in an otherwise susceptible population. In [W. Wang, J. Wang, Analysis of cholera epidemic with bacterial growth and spatial movement, J. Biol. Dyn., 9 (2015), 233-261], a generalized Susceptible-Infected-Recovered-Susceptible-Bacteria (SIRS-B) epidemic model was developed, its R0 was derived, and its ODE version was studied in detail. The authors also introduced its extension to PDE version by including diffusive terms to capture the movement of human hosts and bacteria in a heterogeneous environment and convection term to depict the drift for Vibrio's transport. However, as is often the case, the tools available in ODE do not go through for the PDE case, and many of the results obtained for the ODE case remained unknown for the PDE model. In this talk, we review results from [K. Yamazaki, X. Wang, Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model, Discrete Contin. Dyn. Syst. Ser. B, to appear] in which the global well-posedness as well as the local stability results were obtained for the PDE case by tools from functional, spectral analysis and theory of monotone dynamical system. We also report new results on the global stability case.
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