In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of ${\mathbb{R}}^n$ with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level ${\mathcal{R}}_0\le 1,$ the disease-free equilibrium $E_0$ is globally asymptotically stable. On the other hand, if ${\mathcal{R}}_0>1$ then there exists a unique stable disease equilibrium $E^{\ast }$. The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value ${\mathcal{R}}_0$.

在本文中，我们研究了一种更一般的传染病扩散空间依赖性疫苗接种模型。在我们的扩散疫苗接种模型中，我们考虑了治疗影响和非线性发病率。此外，在该模型中，易感、接种疫苗和感染个体的隔间数量被认为是时间和位置的函数，其中位置集（相当于空间栖息地）是${\mathbb{电阻}}^n$具有平滑的边界。研究了模型的局部和全局稳定性。我们的研究表明，如果阈值水平${\mathcal{电阻}}_0\le 1,$ 无病平衡 ${乙}_0$是全局渐近稳定的。另一方面，如果${\mathcal{电阻}}_0>1$ 那么存在唯一的稳定疾病平衡 ${乙}^{＊}$. 研究了模型解的存在性和一致的持久性结果。最后，使用有限差分格式，我们提出了一些数值例子来验证我们的分析结果。我们的结果表明模型的全局动态完全由阈值决定${\mathcal{电阻}}_0$.