Abstract
<p style='text-indent:20px;'>In this paper, we investigate the threshold results for a nonlocal and time-delayed reaction-diffusion system involving the spatial heterogeneity and the seasonality. Due to the complexity of the model, we rigorously analyze the well-posedness of the model. The basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \Re_0 $\end{document}</tex-math></inline-formula> is characterized with the next generation operator method. We show that the disease-free <inline-formula><tex-math id="M2">\begin{document}$ \omega $\end{document}</tex-math></inline-formula>-periodic solution is globally attractive when <inline-formula><tex-math id="M3">\begin{document}$ \Re_0 &lt; 1 $\end{document}</tex-math></inline-formula>; while the system is uniformly persistent and a positive <inline-formula><tex-math id="M4">\begin{document}$ \omega $\end{document}</tex-math></inline-formula>-periodic solution exists when <inline-formula><tex-math id="M5">\begin{document}$ \Re_0 &gt; 1 $\end{document}</tex-math></inline-formula>. In a special case that the parameters are all independent of the spatial heterogeneity and the seasonality, the global attractivity of the constant equilibria of the model is investigated by the technique of Lyapunov functionals.</p>
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.