A quantitative strong unique continuation property of a diffusive SIS model

This article is concerned with a strong unique continuation property of solutions for a diffusive SIS (Susceptible - Infected - Susceptible, or SI) model, which belongs to a type of observability inequalities in a time interval \begin{document}$ [0, T] $\end{document}. That is, if one can observe solution on a convex and connected bounded open set \begin{document}$ \omega $\end{document} in a bounded domain \begin{document}$ \Omega $\end{document} at time \begin{document}$ t = T $\end{document}, then the norms of solution on \begin{document}$ [0,T) $\end{document} on \begin{document}$ \Omega $\end{document} are observable. In our discussion, boundary condition is a homogeneous Dirichlet one (hostile boundary condition).