International Center for Applied Mathematics and Computational Bioengineering, Department of Mathematics and Natural Sciences, Gulf University for Science & Technology, Mishref, Kuwait.
Department of Mathematics, University of Dayton, Dayton, OH 45469-2316, USA.
Virus Res. 2018 Aug 15;255:95-104. doi: 10.1016/j.virusres.2018.07.002. Epub 2018 Jul 9.
The Zika virus is transmitted to humans primarily through Aedes mosquitoes and through sexual contact. It is documented that the virus can be transmitted to newborn babies from their mothers. We consider a deterministic model for the transmission dynamics of the Zika virus infectious disease that spreads in, both humans and vectors, through horizontal and vertical transmission. The total populations of both humans and mosquitoes are assumed to be constant. Our models consist of a system of eight differential equations describing the human and vector populations during the different stages of the disease. We have included the hospitalization/isolation class in our model to see the effect of the controlling strategy. We determine the expression for the basic reproductive number R in terms of horizontal as well as vertical disease transmission rates. An in-depth stability analysis of the model is performed, and it is consequently shown, that the model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R < 1. It is also shown that when R > 1, there exists a unique endemic equilibrium. We showed that the endemic equilibrium point is globally asymptotically stable when it exists. We were able to prove this result in a reduced model. Furthermore, we conducted an uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R. The uncertainty analysis yields an estimated value of the basic reproductive number R = 1.54. Assuming infection prevalence in the population under constant control, optimal control theory is used to devise an optimal hospitalization/isolation control strategy for the model. The impact of isolation on the number of infected individuals and the accumulated cost is assessed and compared with the constant control case.
寨卡病毒主要通过埃及伊蚊和性接触传播给人类。有记录表明，病毒可以通过母婴传播传染给新生婴儿。我们考虑了一个用于传播动力学的确定性模型，该模型描述了寨卡病毒传染病在人类和媒介中通过水平和垂直传播的传播。假设人类和蚊子的总种群数量保持不变。我们的模型由 8 个微分方程系统组成，描述了疾病不同阶段的人类和蚊子种群。我们在模型中加入了住院/隔离类，以观察控制策略的效果。我们用水平和垂直疾病传播率来确定基本繁殖数 R 的表达式。对模型进行了深入的稳定性分析，结果表明，当基本繁殖数 R < 1 时，模型具有全局渐近稳定的无病平衡点。还表明，当 R > 1 时，存在唯一的地方病平衡点。当存在地方病平衡点时，我们证明了它是全局渐近稳定的。我们在简化模型中证明了这一结果。此外，我们进行了不确定性和敏感性分析，以识别关键模型参数对 R 的影响。不确定性分析得出了基本繁殖数 R = 1.54 的估计值。假设在恒定控制下的人群中感染流行率，最优控制理论被用于为模型设计最优的住院/隔离控制策略。评估了隔离对感染人数和累积成本的影响，并与恒定控制情况进行了比较。
