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首页> 外文期刊>Journal of Mathematical Biology >SI infection on a dynamic partnership network: characterization of R-0
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SI infection on a dynamic partnership network: characterization of R-0

机译：动态伙伴关系网络上的SI感染：R-0的特征

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We model the spread of an (Susceptible Infectious) sexually transmitted infection on a dynamic homosexual network. The network consists of individuals with a dynamically varying number of partners. There is demographic turnover due to individuals entering the population at a constant rate and leaving the population after an exponentially distributed time. Infection is transmitted in partnerships between susceptible and infected individuals. We assume that the state of an individual in this structured population is specified by its disease status and its numbers of susceptible and infected partners. Therefore the state of an individual changes through partnership dynamics and transmission of infection. We assume that an individual has precisely 'sites' at which a partner can be bound, all of which behave independently from one another as far as forming and dissolving partnerships are concerned. The population level dynamics of partnerships and disease transmission can be described by a set of differential equations. We characterize the basic reproduction ratio using the next-generation-matrix method. Using the interpretation of we show that we can reduce the number of states-at-infection to only considering three states-at-infection. This means that the stability analysis of the disease-free steady state of an -dimensional system is reduced to determining the dominant eigenvalue of a matrix. We then show that a further reduction to a matrix is possible where all matrix entries are in explicit form. This implies that an explicit expression for can be found for every value of n.
机译：我们对动态同性恋网络上的（易感性）性传播感染的传播进行建模。该网络由具有动态变化的合作伙伴数量的个人组成。由于个人以恒定的速度进入人口，并在呈指数分布的时间后离开人口，因此出现了人口流动。感染是在易感人群和受感染的个体之间传播的。我们假设此结构化人群中的个体状态由其疾病状况以及易感和受感染的伴侣数量决定。因此，个体的状态通过伙伴关系动态和感染传播而改变。我们假设一个人恰好有一个可以约束合伙人的“场所”，就建立和解除合伙关系而言，所有这些场所都彼此独立。伙伴关系和疾病传播的种群水平动态可以通过一组微分方程来描述。我们使用下一代矩阵方法来表征基本的再生比。使用对的解释，我们可以将感染状态的数量减少到仅考虑三个感染状态。这意味着减少了对多维系统无病稳态的稳定性分析，从而确定了矩阵的主导特征值。然后，我们表明在所有矩阵条目均为显式形式的情况下，可以进一步简化为矩阵。这意味着可以为每个n值找到一个显式表达式。

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