论文标题
具有非线性复发的数学模型：前后背叉的条件
A mathematical model with nonlinear relapse: conditions for a forward-backward bifurcation
论文作者
论文摘要
我们构建了一个易感的改革模型，并探索了改革人群中非线性复发的动态。从易感{\ it处于危险中的{\ it}的过渡是使用严格降低的一般函数建模的，模仿了将流动减少到上瘾类中的影响因素。计算{\ it基本生殖数}。此外，$ r_0 $确定上瘾的平衡的本地渐近稳定性。使用$ r_0 $和其他阈值数量建立了前向后分叉的条件。提出了模型的随机版本，并显示了一些数值示例。结果表明，暂时改革的个体的影响对最初的上瘾人群高度敏感。
We constructed a Susceptible-Addicted-Reformed model and explored the dynamics of nonlinear relapse in the Reformed population. The transition from susceptible considered {\it at-risk} is modeled using a strictly decreasing general function, mimicking an influential factor that reduces the flow into the addicted class. The {\it basic reproductive number} is computed. Furthermore, $R_0$ determines the local asymptotically stability of the addicted-free equilibrium. Conditions for a forward-backward bifurcation were established using $R_0$ and other threshold quantities. A stochastic version of the model is presented, and some numerical examples are shown. Results showed that the influence of the temporarily reformed individuals is highly sensitive to the initial addicted population.
