具有常数潜伏期的随机流行病SEIRS模型
Stochastic epidemic SEIRS models with a constant latency period
摘要：
本文研究了一类确定性和随机性的具有时滞的SEIRS传染病模型的稳定性。事实上，我们假设传输速率可以是随机的，并且在“暴露”的E类个体中存在连续几天的$r$的潜伏期，其中$r$是固定的正整数。通过研究线性化系统的特征值，得到了无病平衡点在有时滞和无时滞两种情况下的稳定性条件。在后一种情况下，我们也得到了共存平衡点稳定的条件。在随机的情况下，我们能够推导出一个浓度的随机波动的结果，然后，使用李雅普诺夫方法，在适当的假设下，免费的疾病平衡仍然是稳定的。
英文摘要：
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive days, where $r$ is a fixed positive integer, in the "exposed" individuals class E. Studying the eigenvalues of the linearized system, we obtain conditions for the stability of the free disease equilibrium, in both the cases of the deterministic model with and without delay. In this latter case, we also get conditions for the stability of the coexistence equilibrium. In the stochastic case we are able to derive a concentration result for the random fluctuations and then, using the Lyapunov method, that under suitable assumptions the free disease equilibrium is still stable.
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