| Abstract: |
| In this talk, we shall discuss an SIS modelwith a cross-diffusion dispersal strategy for the infected individuals describing the public health intervention measures (like quarantine) during the outbreak of infectious diseases. The model adopts the frequency-dependent transmission mechanism and includes demographic changes (i.e. population recruitment and death) subject to homogeneous Neumann boundary conditions. We establish the existence of globally bounded classical solutions and define the basic reproduction number $R_0$ by a weighted variational form. by a change of variable and the index theory along with the principal eigenvalue theory, we establish the threshold dynamics in terms of $R_0$. The global stability of the unique disease-free equilibrium and constant endemic equilibrium under some conditions is also obtained. Finally, we discuss some open questions and use numerical simulation to demonstrate the applications of our analytical results. |
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