Miyaoka Tiago Yuzo, Lenhart Suzanne, Meyer João F C A
Department of Applied Mathematics, IMECC, University of Campinas, Campinas, SP, Brazil.
Department of Mathematics, University of Tennessee, Knoxville, TN, USA.
J Math Biol. 2019 Aug;79(3):1077-1104. doi: 10.1007/s00285-019-01390-z. Epub 2019 Jun 11.
Zika virus has acquired worldwide concern after a recent outbreak in Latin America that started in Brazil, with associated neurological conditions such as microcephaly in newborns from infected mothers. The virus is transmitted mainly by Aedes aegypti mosquitoes, but direct (sexual) transmission has been documented. We formulate a reaction diffusion model that considers spatial movement of humans and vectors, with local contact transmission of Zika virus. Vaccination is introduced as a control variable, giving immunity to susceptible humans, in order to characterize an optimal vaccination strategy that minimizes the costs associated with infections and vaccines. The optimal control characterization is obtained in terms of state and adjoint equations. Parameter estimation and numerical simulations are carried out using data for the initial 2015 Zika outbreak in the state of Rio Grande do Norte in Brazil. Several scenarios are considered and analyzed in terms of number of new infections and costs, showing that the optimal control application is successful, significantly reducing these quantities.
在最近始于巴西并在拉丁美洲爆发后，寨卡病毒已引起全球关注，此次爆发伴有诸如受感染母亲所生新生儿小头畸形等相关神经疾病。该病毒主要通过埃及伊蚊传播，但已有直接（性）传播的记录。我们构建了一个反应扩散模型，该模型考虑人类和病媒的空间移动以及寨卡病毒的局部接触传播。引入疫苗接种作为控制变量，使易感人群获得免疫力，以确定一种最优的疫苗接种策略，该策略能将与感染和疫苗相关的成本降至最低。最优控制特征是根据状态方程和伴随方程得到的。利用巴西北里奥格兰德州2015年寨卡病毒首次爆发的数据进行了参数估计和数值模拟。根据新感染病例数和成本考虑并分析了几种情况，结果表明最优控制的应用是成功的，显著减少了这些数量。
