In a planar smoothly bounded domain $\Omega$ , we consider the model for oncolytic virotherapy given by $$\left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) - uz, \\[1mm] v_t = - (u+w)v, \\[1mm] w_t = d_w \Delta w - w + uz, \\[1mm] z_t = d_z \Delta z - z - uz + \beta w, \end{array} \right.$$ with positive parameters $ D_w $ , $ D_z $ and $\beta$ . It is firstly shown that whenever $\beta \lt 1$ , for any choice of $M \gt 0$ , one can find initial data such that the solution of an associated no-flux initial-boundary value problem, well known to exist globally actually for any choice of $\beta \gt 0$ , satisfies $$u\ge M \qquad \mbox{in } \Omega\times (0,\infty).$$ If $\beta \gt 1$ , however, then for arbitrary initial data the corresponding is seen to have the property that $$\liminf_{t\to\infty} \inf_{x\in\Omega} u(x,t)\le \frac{1}{\beta-1}.$$ This may be interpreted as indicating that $\beta$ plays the role of a critical virus replication rate with regard to efficiency of the considered virotherapy, with corresponding threshold value given by $\beta = 1$ .

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溶瘤病毒治疗效率的关键病毒产生率

在平面平滑有界域中$\欧米茄$，我们考虑溶瘤病毒疗法的模型$$\left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) - uz, \\[1mm] v_t = - (u+w)v, \\ [1mm] w_t = d_w \Delta w - w + uz, \\[1mm] z_t = d_z \Delta z - z - uz + \beta w, \end{array} \right.$$具有正参数$ D_w $,$ D_z $和$\beta$. 首先表明，每当$\beta \lt 1$, 对于任何选择$M \gt 0$，可以找到初始数据，使得相关的无通量初始边界值问题的解，众所周知，实际上对于任何选择$\beta \gt 0$, 满足$$u\ge M \qquad \mbox{in } \Omega\times (0,\infty).$$如果$\beta \gt 1$，然而，对于任意初始数据，对应的被视为具有以下属性$$\liminf_{t\to\infty} \inf_{x\in\Omega} u(x,t)\le \frac{1}{\beta-1}.$$这可以解释为表明$\beta$在所考虑的病毒疗法的效率方面起着关键病毒复制率的作用，相应的阈值由下式给出$\beta = 1$.