Allen Linda J S, Schwartz Elissa J
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States.
School of Biological Sciences and Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States.
Math Biosci. 2015 Dec;270(Pt B):237-48. doi: 10.1016/j.mbs.2015.04.001. Epub 2015 Apr 10.
Equine infectious anemia virus (EIAV) is a lentivirus in the retrovirus family that infects horses and ponies. Two strains, referred to as the sensitive strain and the resistant strain, have been isolated from an experimentally-infected pony. The sensitive strain is vulnerable to neutralization by antibodies whereas the resistant strain is neutralization-insensitive. The sensitive strain mutates to the resistant strain. EIAV may infect healthy target cells via free virus or alternatively, directly from an infected target cell through cell-to-cell transfer. The proportion of transmission from free-virus or from cell-to-cell transmission is unknown. A system of ordinary differential equations (ODEs) is formulated for the virus-cell dynamics of EIAV. In addition, a Markov chain model and a branching process approximation near the infection-free equilibrium (IFE) are formulated. The basic reproduction number R0 is defined as the maximum of two reproduction numbers, R0s and R0r, one for the sensitive strain and one for the resistant strain. The IFE is shown to be globally asymptotically stable for the ODE model in a special case when the basic reproduction number is less than one. In addition, two endemic equilibria exist, a coexistence equilibrium and a resistant strain equilibrium. It is shown that if R0>1, the infection persists with at least one of the two strains. However, for small infectious doses, the sensitive strain and the resistant strain may not persist in the Markov chain model. Parameter values applicable to EIAV are used to illustrate the dynamics of the ODE and the Markov chain models. The examples highlight the importance of the proportion of cell-to-cell versus free-virus transmission that either leads to infection clearance or to infection persistence with either coexistence of both strains or to dominance by the resistant strain.
马传染性贫血病毒（EIAV）是逆转录病毒科中的一种慢病毒，可感染马和矮种马。从一匹实验感染的矮种马中分离出了两种毒株，分别称为敏感株和抗性株。敏感株易被抗体中和，而抗性株对中和不敏感。敏感株会突变为抗性株。EIAV可通过游离病毒感染健康靶细胞，或者直接从受感染的靶细胞通过细胞间转移进行感染。游离病毒传播或细胞间传播的比例尚不清楚。针对EIAV的病毒 - 细胞动力学建立了一个常微分方程（ODE）系统。此外，还建立了一个马尔可夫链模型以及在无感染平衡点（IFE）附近的分支过程近似模型。基本再生数R0被定义为两个再生数R0s和R0r中的最大值，一个对应敏感株，另一个对应抗性株。在基本再生数小于1的特殊情况下，对于ODE模型，IFE被证明是全局渐近稳定的。此外，存在两个地方病平衡点，一个共存平衡点和一个抗性株平衡点。结果表明，如果R0>1，感染会在两种毒株中的至少一种毒株中持续存在。然而，对于小感染剂量，敏感株和抗性株在马尔可夫链模型中可能不会持续存在。适用于EIAV的参数值被用于说明ODE模型和马尔可夫链模型的动力学。这些例子突出了细胞间传播与游离病毒传播的比例的重要性，该比例要么导致感染清除，要么导致感染持续存在，要么两种毒株共存，要么抗性株占主导。
