Fig. 5
The global stability of disease-free equilibrium of temporal-spatial heterogeneity system (1) when \(\beta _{1} \left( x,t\right) =0.6e^{-x},\beta _{2}\left( x,t\right) =0.3e^{-2x}\left| \sin xt\right| ,\gamma \left( x,t\right) =0.223\left| \cos x\right| ,\rho _{2}\left( x,t\right) =0.02\left| \sin x\right| ,\eta _{2}\left( x,t\right) =0.157e^{-2xt}\)