A very important population threshold quantity is the target reproduction number, which is a measure of control effort required for a target prevention, intervention or control. This concept, as a generalization of type reproduction number, was first introduced in Shuai et al. (J Math Biol 67:1067–1082, 2013) for nonnegative matrices with immediate applications to compartmental population models of ordinary differential equations. The current paper is devoted to the study of all target reproduction numbers for reaction-diffusion population models with compartmental structure. It turns out that the target reproduction number can be regarded as the basic reproduction number of a modified system, where the state of newborn individuals is limited to the target control set and the offspring from the non-target set is regarded as a part of the transition. In other words, the target reproduction number can be interpreted as the expected number of offspring in a specific target set that a primary newborn individual of the same set would produce during its lifetime. We also characterize the target reproduction number so that it can be easily computed numerically for reaction-diffusion models. At the end, we demonstrate our theoretical observations using two examples.

一个非常重要的种群阈值数量是目标繁殖数量，它是目标预防，干预或控制所需的控制努力的量度。这个概念，作为类型复制数的概括，首先在Shuai等人中引入。（J Math Biol 67：1067–1082，2013）用于非负矩阵，可立即应用于常微分方程的分区人口模型。本文致力于研究具有间隔结构的反应扩散种群模型的所有目标繁殖数。事实证明，目标再现号可以看作是修改系统的基本再现号，新生儿的状态仅限于目标对照组，而非目标组的后代则被视为过渡的一部分。换句话说，目标繁殖数量可以解释为特定目标种群中预期的后代数目，该特定目标种群中同一种群的初生新生儿在其一生中将产生的后代数目。我们还对目标复制数进行了表征，以便可以轻松地对反应扩散模型进行数值计算。最后，我们用两个例子来证明我们的理论观察。我们还对目标复制数进行了表征，以便可以轻松地对反应扩散模型进行数值计算。最后，我们用两个例子来证明我们的理论观察。我们还对目标复制数进行了表征，以便可以轻松地对反应扩散模型进行数值计算。最后，我们用两个例子来证明我们的理论观察。