Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, USA.
J Theor Biol. 2020 Apr 21;491:110194. doi: 10.1016/j.jtbi.2020.110194. Epub 2020 Feb 8.
As standard mathematical models for the transmission of vector-borne pathogens with weak or no apparent sterilizing immunity, Susceptible-Infected-Susceptible (SIS) systems such as the Ross-Macdonald equations are a useful starting point for modeling the impacts of interventions on prevalence for diseases that cannot superinfect their hosts. In particular, they are parameterizable from quantities we can estimate such as the force of infection (FOI), the rate of natural recovery from a single infection, the treatment rate, and the rate of demographic turnover. However, malaria parasites can superinfect their host which has the effect of increasing the duration of infection before total recovery. Queueing theory has been applied to capture this behavior, but a problem with current queueing models is the exclusion of factors such as demographic turnover and treatment. These factors in particular can affect the entire shape of the distribution of the multiplicity of infection (MOI) generated by the superinfection process, its transient dynamics, and the population mean recovery rate. Here we show the distribution of MOI can be described by an alternative hyper-Poisson distribution. We then couple our resulting equations to a simple vector transmission model, extending previous Ross-Macdonald theory.
作为带有弱或无明显绝育免疫的病媒传播病原体的标准数学模型，如 Ross-Macdonald 方程的易感-感染-易感 (SIS) 系统，是对无法再次感染宿主的疾病进行干预对流行率影响建模的一个有用起点。特别是，它们可以根据我们可以估计的数量进行参数化，例如感染力 (FOI)、单次感染自然恢复率、治疗率和人口更替率。然而，疟原虫可以再次感染宿主，这会增加感染完全恢复前的持续时间。排队论已被应用于捕捉这种行为，但当前排队模型的一个问题是排除了人口更替和治疗等因素。这些因素尤其会影响由再感染过程产生的感染多重性 (MOI) 的分布、其瞬态动力学和群体平均恢复率的整个形状。在这里，我们展示了 MOI 的分布可以用替代的超泊松分布来描述。然后，我们将得到的方程与一个简单的向量传播模型相结合，扩展了之前的 Ross-Macdonald 理论。
