| Abstract: |
| This talk presents the invasion dynamics of a time-periodic reaction-diffusion SI model with a free boundary. Employing the theory of time-varying domains and internally chain transitive sets, we rigorously establish a spreading-vanishing dichotomy for both the host population and the disease, and derive sharp criteria characterizing the conditions for spreading and vanishing. Furthermore, in the spreading scenario, we determine the asymptotic speed of the expanding population front, and compare it with the spreading speed of disease invasion. Various scenarios are presented to examine whether the speed of disease invasion can match that of host expansion, with corresponding sharp conditions provided. Further numerical simulations will be presented to validate theoretical results. |
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