Rogers D J
Department of Zoology, University of Oxford.
Parasitology. 1988 Aug;97 ( Pt 1):193-212. doi: 10.1017/s0031182000066853.
A general mathematical model of a vector-borne disease involving two vertebrate host species and one insect vector species is described. The model is easily extended to other situations involving more than two hosts and one vector species. The model, which was developed from the single-host model for malaria described by Aron & May (1982), is applied to the African trypanosomiases and allows for incubation and immune periods in the two host species and for variable efficiency of transmission of different trypanosome species from the vertebrates to the vectors and vice versa. Equations are derived for equilibrium disease prevalence in each of the species involved. Model predictions are examined by 3-dimensional phase-plane analysis, which is presented as a simple extension of the 2-dimensional phase-plane analysis of the malaria model. Parameter values appropriate for the African trypanosomiases are derived from the literature, and a typical West African village situation is considered, with 300 humans, 50 domestic animals and an average population of 5000 tsetse flies. The model predicts equilibrium prevalences of Trypanosoma vivax, T. congolense and T. brucei of 47.0, 45.8 and 28.7% respectively in the animal hosts, 24.2, 3.4 and 0.15% in the tsetse vectors, and a 7.0% infection of humans with human-infective T. brucei. The contribution to the basic rate of reproduction of the human-infective T. brucei is only 0.11 from the human hosts and 2.54 from the animal hosts, indicating that in the situation modelled human sleeping sickness cannot be maintained in the human hosts alone. The animal reservoir is therefore crucial in determining not only the continued occurrence of the disease in humans, but its prevalence in these hosts as well. The effect of changing average fly density on equilibrium disease prevalences is examined, together with the effect of seasonal changes in fly numbers on disease incidence. In a seasonal situation changes in fly mortality rates affect both future population size and infection rate. Peak disease incidence lags behind peak fly numbers, and that in the less favoured host lags behind that in the more favoured host. Near the threshold fly density for disease transmission disease incidence is more changeable than at higher fly densities and may even exceed equilibrium prevalence at the same average fly density (because most hosts are susceptible at the time that fly numbers begin their annual increase).(ABSTRACT TRUNCATED AT 400 WORDS)
描述了一种涉及两种脊椎动物宿主物种和一种昆虫媒介物种的虫媒疾病通用数学模型。该模型可轻松扩展到涉及两种以上宿主和一种媒介物种的其他情况。此模型是在Aron和May（1982年）描述的疟疾单宿主模型基础上开发的，应用于非洲锥虫病，考虑了两种宿主物种的潜伏期和免疫期，以及不同锥虫物种从脊椎动物到媒介和反之从媒介到脊椎动物的不同传播效率。推导了所涉及的每个物种的疾病平衡流行率方程。通过三维相平面分析来检验模型预测，它是疟疾模型二维相平面分析的简单扩展。适合非洲锥虫病的参数值取自文献，并考虑了典型的西非村庄情况，有300人、50头家畜和平均5000只采采蝇的种群。该模型预测，在动物宿主中，间日锥虫、刚果锥虫和布氏锥虫的平衡流行率分别为47.0%、45.8%和28.7%，在采采蝇媒介中分别为24.2%、3.4%和0.15%，感染人类的布氏锥虫导致人类感染率为7.0%。感染人类的布氏锥虫对基本繁殖率的贡献，来自人类宿主的仅为0.11，来自动物宿主的为2.54，这表明在所模拟的情况下，人类昏睡病仅靠人类宿主无法维持。因此，动物宿主不仅对于疾病在人类中的持续发生至关重要，对于其在这些宿主中的流行率也至关重要。研究了平均采采蝇密度变化对疾病平衡流行率的影响，以及采采蝇数量季节性变化对疾病发病率的影响。在季节性情况下，采采蝇死亡率的变化会影响未来种群规模和感染率。疾病发病率峰值滞后于采采蝇数量峰值，较不偏好宿主中的发病率峰值滞后于较偏好宿主中的发病率峰值。在疾病传播的阈值采采蝇密度附近，疾病发病率比在较高采采蝇密度时更易变化，甚至可能超过相同平均采采蝇密度下的平衡流行率（因为在采采蝇数量开始年度增加时，大多数宿主易感）。
