An outbreak vector-host epidemic model with spatial structure: the 2015-2016 Zika outbreak in Rio De Janeiro.

Q1 Mathematics
W E Fitzgibbon, J J Morgan, G F Webb
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引用次数: 1

Abstract

Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors to susceptible hosts through criss-cross dynamics. The model is focused on an outbreak that arises from a small number of infected hosts imported into a subregion of the geographical setting. The goal is to understand how spatial heterogeneity of the vector and host populations influences the dynamics of the outbreak, in both the geographical spread and the final size of the epidemic.

Methods: Partial differential equations are formulated to describe the spatial interaction of the hosts and vectors. The partial differential equations have reaction-diffusion terms to describe the criss-cross interactions of hosts and vectors. The partial differential equations of the model are analyzed and proven to be well-posed. A local basic reproduction number for the epidemic is analyzed.

Results: The epidemic outcomes of the model are correlated to the spatially dependent parameters and initial conditions of the model. The partial differential equations of the model are adapted to seasonality of the vector population, and applied to the 2015-2016 Zika seasonal outbreak in Rio de Janeiro Municipality in Brazil.

Conclusions: The results for the model simulations of the 2015-2016 Zika seasonal outbreak in Rio de Janeiro Municipality indicate that the spatial distribution and final size of the epidemic at the end of the season are strongly dependent on the location and magnitude of local outbreaks at the beginning of the season. The application of the model to the Rio de Janeiro Municipality Zika 2015-2016 outbreak is limited by incompleteness of the epidemic data and by uncertainties in the parametric assumptions of the model.

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具有空间结构的暴发媒介-宿主流行模型:2015-2016年巴西里约热内卢寨卡疫情
背景:为流行病在地理环境中的空间传播建立了一个确定性模型。该疾病通过交叉动力学由病媒传播给易感宿主。该模型侧重于将少量受感染宿主输入地理环境的一个分区域而引起的疫情。目标是了解媒介和宿主种群的空间异质性如何影响疫情的动态,包括疫情的地理传播和最终规模。方法:用偏微分方程来描述宿主与载体的空间相互作用。偏微分方程有反应扩散项来描述宿主和矢量的交叉相互作用。对模型的偏微分方程进行了分析,证明了其适定性。分析了该流行病的局部基本再现数。结果:模型的流行结果与模型的空间依赖参数和初始条件相关。该模型的偏微分方程适应了病媒种群的季节性,并应用于2015-2016年巴西里约热内卢市寨卡病毒季节性暴发。结论:2015-2016年里约热内卢市寨卡病毒季节性暴发的模型模拟结果表明,寨卡病毒季末暴发的空间分布和最终规模与寨卡病毒季初暴发的地点和规模密切相关。该模型在里约热内卢市2015-2016年寨卡疫情中的应用受到流行病数据不完整和模型参数假设不确定的限制。
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来源期刊
Theoretical Biology and Medical Modelling
Theoretical Biology and Medical Modelling MATHEMATICAL & COMPUTATIONAL BIOLOGY-
自引率
0.00%
发文量
0
审稿时长
6-12 weeks
期刊介绍: Theoretical Biology and Medical Modelling is an open access peer-reviewed journal adopting a broad definition of "biology" and focusing on theoretical ideas and models associated with developments in biology and medicine. Mathematicians, biologists and clinicians of various specialisms, philosophers and historians of science are all contributing to the emergence of novel concepts in an age of systems biology, bioinformatics and computer modelling. This is the field in which Theoretical Biology and Medical Modelling operates. We welcome submissions that are technically sound and offering either improved understanding in biology and medicine or progress in theory or method.
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