In this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

中文翻译：

---

二手烟的敏感性及数学模型分析

在本文中，我们关注的是二手烟者的数学模型。该模型具有生物学意义，并且在数学上是合适的。再生数 $$R_{0}$$ R 0 由模型确定，它衡量完全易感人群中单个原发病例产生的继发病例平均数。如果$$R_{0}<1,$$R 0 < 1 ，则无烟平衡点稳定，如果$$R_{0}>1,$$ R 0 > 1 ，则地方病平衡点不稳定。我们还提供数值模拟来显示平衡点的稳定性。此外，还包括对所提出模型的动态系统中涉及的参数的敏感性分析。涉及再生数的参数衡量参数值变化时$$R_{0}$$R 0 的相对变化。