Modeling and Dynamics Analysis of Zika Transmission with Limited Medical Resources
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Modeling and Dynamics Analysis of Zika Transmission with Limited Medical Resources Hongyong Zhao1
· Liping Wang1 · Sergio Muniz Oliva2 · Huaiping Zhu3
Received: 29 October 2019 / Accepted: 8 July 2020 © Society for Mathematical Biology 2020
Abstract Zika virus, a reemerging mosquito-borne flavivirus, posed a global public health emergency in 2016. Brazil is the most seriously affected country. Some measures have been implemented to control the Zika transmission, such as spraying mosquitoes, developing vaccines and drugs. However, because of the limited medical resources (LMRs) in the country, not every infected patient can be treated in time when infected with Zika virus. We aim to build a deterministic Zika model by introducing a piecewise smooth treatment recovery rate to research the effect of LMRs on the transmission and control of Zika. For the model without treatment, we analyze the global stability of equilibria. For the model with treatment, the model exhibits complex dynamics. We prove that the model with treatment undergoes backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation of codimension 2. It means that the model with LMRs is sensitive to parameters and initial conditions, which has important significance for control of Zika. We also apply the model to estimate the basic and control reproduction numbers for the Zika transmission by using the data on weekly reported accumulated Zika cases from March 25, 2016, to April 14, 2018, in Brazil. Keywords Zika virus · Medical resources · Mosquito-borne and sexual transmission · Backward bifurcation · Hopf bifurcation · Bogdanov–Takens bifurcation Mathematics Subject Classification 34C23 · 34D20 · 34C40
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Hongyong Zhao [email protected]
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Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China
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Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP CEP 05508-090, Brazil
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Lamps and Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada 0123456789().: V,-vol
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1 Introduction Zika virus is a reemerging mosquito-borne pathogen initially isolated from rhesus monkeys in the Zika forest, Uganda, in 1947 (Dick et al. 1952). The first case of human infection was reported in Nigeria in 1954 (Dick et al. 1952). The next 50 years, Zika has been quietly circulating in several countries in equatorial Africa and Asia. Few human cases were reported prior to the first recorded outbreak on Yap Island, Micronesia, in April–July 2007 (Duffy 2009). Subsequently, after that in 2013, an outbreak occurred in French Polynesia, with estimated approximately 28,000 infected individuals (Cao-Lormeau and Musso 2014). From then on, Zika virus was not anymore a minor infection restricted to Africa and Asia (Campos et al. 2015; Roa 2016). It has quickly spread to all continents, swept through Central and southern America and a
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