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The threshold of a deterministic and a stochastic SIQS epidemic model with varying total population size

机译：确定性和随机SIQS流行病模型的阈值，具有不同的总群体大小

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In this paper, a stochastic and a deterministic SIS epidemic model with isolation and varying total population size are proposed. For the deterministic model, we establish the threshold R_0. When R_0 is less than 1, the disease-free equilibrium is globally stable, which means the disease will die out. While R_0 is greater than 1, the endemic equilibrium is globally stable, which implies that the disease will spread. Moreover, there is a critical isolation rate S", when the isolation rate is greater than it, the disease will be eliminated. For the stochastic model, we also present its threshold R_(0s). When R_(0s) is less than 1, the disease will disappear with probability one. While R_(0s) is greater than 1, the disease will persist. We find that stochastic perturbation of the transmission rate (or the valid contact coefficient) can help to reduce the spread of the disease. That is, compared with stochastic model, the deterministic epidemic model overestimates the spread capacity of disease. We further find that there exists a critical the stochastic perturbation intensity of the transmission rate σ*, when the stochastic perturbation intensity of the transmission rate is bigger than it, the disease will disappear. At last, we apply our theories to a realistic disease, pneumococcus amongst homosexuals, carry out numerical simulations and obtain the empirical probability density under different parameter values. The critical isolation rate δ* is presented. When the isolation rate S is greater than S', the pneumococcus amongst will be eliminated.
机译：在本文中，提出了一种具有隔离和变化总群体大小的随机和确定性的SIS流行病模型。对于确定性模型，我们建立了阈值r_0。当R_0小于1时，无疾病平衡是全球稳定的，这意味着这种疾病会消失。虽然R_0大于1，但流行均衡是全球稳定的，这意味着疾病将传播。此外，存在临界分离率S“，当隔离速率大于它时，疾病将被淘汰。对于随机模型，我们还呈现其阈值R_（0s）。当r_（0s）小于1时，疾病将与概率消失。虽然R_（0s）大于1，但疾病将持续存在。我们发现传输速率（或有效接触系数）的随机扰动可以有助于降低疾病的扩散。也就是说，与随机模型相比，确定性流行病模型高估了疾病的传播能力。我们进一步发现，当传动速率的随机扰动强度大于时，透射率σ*的随机扰动强度都存在临界。它，这种疾病会消失。最后，我们将我们的理论应用于现实疾病，在同性恋中的肺炎球菌，进行数值模拟，并获得不同议定书下的经验概率密度仪表值。临界隔离速率Δ*呈现。当分离率S大于S'时，将消除肺炎球菌。

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