Abstract Considering the individual differences, spatial environment and the temporary acquired immunity, a general multi-group reaction–diffusion epidemic model with nonlinear incidence and temporary acquired immunity is proposed in this paper. The well-posedness of the solution including the existence of global solutions and the ultimate boundedness of the solutions are obtained, and then we define the basic reproduction number R 0 . Further, the threshold dynamics of the disease are obtained in terms of R 0 . Moreover, by constructing suitable Lyapunov functions, we obtain the endemic steady state is globally asymptotically stable in homogeneous space and heterogeneous case when R 0 > 1 . Based on theoretical analysis, we conclude that the existence of immunity loss rate and the difference of diffusion rate may bring great difficulties to control the disease. Finally, we find the spatial heterogeneity cannot always enhance the infectious risk of the disease and simply increasing the diffusion coefficient cannot effectively control the spread of the disease via some numerical simulations.

中文翻译：

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具有非线性发病率和暂时获得性免疫的一般多组反应-扩散流行病模型分析

摘要 考虑个体差异、空间环境和暂时性获得性免疫，提出了具有非线性发病率和暂时性获得性免疫的一般多群体反应-扩散流行模型。得到解的适定性，包括全局解的存在性和解的极限有界，然后定义基本再生数R 0 。此外，根据R 0 获得疾病的阈值动态。此外，通过构建合适的李雅普诺夫函数，当 R 0 > 1 时，我们获得了在同质空间和异质情况下局部稳定状态是全局渐近稳定的。根据理论分析，我们得出结论，免疫丧失率的存在和扩散率的差异可能会给疾病的控制带来很大的困难。最后，我们通过一些数值模拟发现，空间异质性并不总是会增加疾病的传染风险，单纯增加扩散系数也不能有效控制疾病的传播。