Saad-Roy C M, Ma Junling, van den Driessche P
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.
J Math Biol. 2018 Dec;77(6-7):1917-1941. doi: 10.1007/s00285-018-1230-1. Epub 2018 Apr 25.
Zika virus is a human disease that may lead to neurological disorders in affected individuals, and may be transmitted vectorially (by mosquitoes) or sexually. A mathematical model of Zika virus transmission is formulated, taking into account mosquitoes, sexually active males and females, inactive individuals, and considering both vector transmission and sexual transmission from infectious males to susceptible females. Basic reproduction numbers are computed, and disease control strategies are evaluated. The effect of the incidence function used to model sexual transmission from infectious males to susceptible females is investigated. It is proved that for such functions that are sublinear, if the basic reproduction [Formula: see text], then the disease dies out and [Formula: see text] is a sharp threshold. Moreover, under certain conditions on model parameters and assuming mass action incidence for sexual transmission, it is proved that if [Formula: see text], there exists a unique endemic equilibrium that is globally asymptotically stable. However, under nonlinear incidence, it is shown that for certain functions backward bifurcation and Hopf bifurcation may occur, giving rise to subthreshold equilibria and periodic solutions, respectively. Numerical simulations for various parameter values are displayed to illustrate these behaviours.
寨卡病毒是一种可导致受感染个体出现神经紊乱的人类疾病，它可通过媒介（蚊子）传播或性传播。构建了一个寨卡病毒传播的数学模型，该模型考虑了蚊子、有性活动的男性和女性、非活动个体，并兼顾了媒介传播以及从感染男性到易感女性的性传播。计算了基本再生数，并评估了疾病控制策略。研究了用于模拟从感染男性到易感女性性传播的发病率函数的影响。结果证明，对于此类次线性函数，如果基本再生数[公式：见原文]，那么疾病会消亡，且[公式：见原文]是一个尖锐阈值。此外，在模型参数的某些条件下，并假设性传播的质量作用发病率，结果证明如果[公式：见原文]，则存在唯一的地方病平衡点，该平衡点是全局渐近稳定的。然而，在非线性发病率情况下，结果表明对于某些函数可能会出现反向分支和霍普夫分支，分别产生亚阈值平衡点和周期解。展示了针对各种参数值的数值模拟，以说明这些行为。
