Stability Analyses of the Stochastic Delayed Infectious Models with Reinfection
Stability Analyses of the Stochastic Delayed Infectious Models with Reinfection
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DOI：
10.5687/iscie.32.1
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发表时间：
2019-01
期刊：
影响因子：
--
通讯作者：
M. Ishikawa
中科院分区：
文献类型：
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作者：
M. Ishikawa
目前，也门爆发了前所未有的霍乱疫情，在医疗技术高度发达的社会，各种传染病仍然威胁着我们。因此，制定控制传染病传播的战略势在必行。病媒传播的疾病，例如疟疾和登革热，在传播疾病时，由于病媒的病毒发展有潜伏期，所以会有时间上的延迟。应该注意的是，在传染病如疟疾中有再次感染的可能性。此外，在现实的传染病传播过程中，环境变化和个体差异会导致感染率、治愈率和接种效果的随机波动。考虑到这些事实，我们提出了两类具有再感染的随机时滞传染病模型。由于传染病的传播与随机传染病模型的无病稳态（DFS）的稳定性有关，本文利用随机李雅普诺夫定理分析了无病稳态的稳定性。通过计算李雅普诺夫指数，数值模拟研究了传染病模型中随机噪声对各种群行为的影响。
At present, the unprecedented cholera outbreak occurs in Yemen and various kinds of infectious diseases are still threat to us in the high-developed medical technology society. Hence, the strategization to control the spread of the infectious diseases becomes imperative. In the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. It should be noted that there is possibility of getting reinfected in the infectious disease such as malaria. Moreover, in the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection, the recovery rates and the vaccination effect. Taking these facts into consideration, we propose two types of the stochastic delayed infectious models with reinfection. Since the spread of infection has reference to the stability of the disease-free steady state (DFS) of the stochastic infectious models, we analyze the stability of the DFS by using the stochastic Lyapunov theorem. By calculating the Lyapunov exponent, we study the influence of the random noise in the infectious model on each population behavior by numerical simulations.