论文标题
随机SICA流行模型与跳跃过程
Stochastic SICA Epidemic Model with Jump Lévy Processes
论文作者
论文摘要
我们提出并研究了一个转移的SICA流行模型，将Silva和Torres（2017）扩展到了由Brownian运动过程和JumpLévy噪声驱动的随机设置。流行病学中的数学建模作品通常会忽略Lévy噪声扰动，但是由于HIV/AIDS动力学中存在强大的波动，因此它将其纳入SICA流行模型值得考虑，通常导致在研究过程中出现了许多不连续性。我们的工作如下：（i）我们首先介绍模型，清楚地证明其使用的形式是合理的，即与Lévy噪声相关的组件； （ii）我们通过构建合适的停止时间来证明全球积极解决方案的存在和独特性； （iii）在某些假设下，我们显示出艾滋病毒/艾滋病的灭绝； （iv）我们获得足够的条件，以确保艾滋病毒/艾滋病的持久性； （v）我们通过数值模拟说明了我们的数学结果。
We propose and study a shifted SICA epidemic model, extending the one of Silva and Torres (2017) to the stochastic setting driven by both Brownian motion processes and jump Lévy noise. Lévy noise perturbations are usually ignored by existing works of mathematical modelling in epidemiology, but its incorporation into the SICA epidemic model is worth to consider because of the presence of strong fluctuations in HIV/AIDS dynamics, often leading to the emergence of a number of discontinuities in the processes under investigation. Our work is organised as follows: (i) we begin by presenting our model, by clearly justifying its used form, namely the component related to the Lévy noise; (ii) we prove existence and uniqueness of a global positive solution by constructing a suitable stopping time; (iii) under some assumptions, we show extinction of HIV/AIDS; (iv) we obtain sufficient conditions assuring persistence of HIV/AIDS; (v) we illustrate our mathematical results through numerical simulations.
