No abstract

No abstract

No abstract

Decorating the In2S3 nanosheets with in situ formed In nanoparticles boosted the CO2 electroreduction.

<p style='text-indent:20px;'>A diffusion SEIAR model with Beddington-DeAngelis type incidence is proposed to characterize the spread of COVID-19 with spatial transmission. First, the well-posedness of solution is studied. Second, the basic reproduction number <inline-formula><tex-math id="M3">\begin{document}$ \mathcal R_{0} $\end{document}</tex-math></inline-formula> is derived and served as a threshold value to determine whether COVID-19 will spread. Meanwhile, we consider the effect of diffusion on the spread of COVID-19 in spatial homogenous environment, by which we can obtain that if <inline-formula><tex-math id="M4">\begin{document}$ \mathcal R_{0}&lt;1 $\end{document}</tex-math></inline-formula>, then the infection-free steady state is globally asymptotically stable, while if <inline-formula><tex-math id="M5">\begin{document}$ \mathcal R_{0}&gt;1 $\end{document}</tex-math></inline-formula>, then the endemic steady state is globally asymptotically stable. Furthermore, according to the official reporting data about COVID-19 in Wuhan, China, the actual value of <inline-formula><tex-math id="M6">\begin{document}$ \mathcal R_{0} $\end{document}</tex-math></inline-formula> is estimated, and comparing with other types of incidence, we find that the estimated peak with Beddington-DeAngelis type incidence is more close to the cases in reality. Finally, by numerical simulations, we can see that the diffusion behavior has evident impact on the spread of COVID-19 in spatial heterogeneity than homogeneity of environment.</p>

In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie-Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the positive periodic solutions are established. Moreover, the existence region of the positive periodic solutions is an invariant region dependent on t. Then, constructing a suitable Lyapunov function, we obtain sufficient conditions to guarantee the global asymptotic stability of the positive periodic solutions. Finally, we do some numerical simulations to verify our main results and investigate the effect of prey refuge on the dynamics of the system.

No abstract

No abstract