Lyapunov Functions and Qualitative Analysis of an Epidemic Model with Vaccination.

The spatial-temporal diffusion dynamics of infectious disease with vaccination therapy are studied through a mathematical model. We have investigated the well-posedness, disease-free equilibrium, disease equilibrium, the existence and the uniqueness of solutions, and the calculation of basic reproduction numbers by Jacobian matrix. After that, the positivity, as well as boundedness of solutions, are also established. The global stability of diseasefree and steady-state disease results is established by utilizing compatible Lyapunov functions and LaSalle's invariance principle. Illustration of the numerical examples to show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail. [ABSTRACT FROM AUTHOR]