Department of Mathematics, Washington State University, Pullman, WA 99164, USA.
Department of Mathematics and Statistics, Queen's University, Kingston, ON K7L 3N6, Canada.
Viruses. 2023 Mar 6;15(3):691. doi: 10.3390/v15030691.
Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube sampling and least squares to find the parameter ranges that equally divide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.
马传染性贫血病毒（EIAV）是马属动物的一种重要感染，其与 HIV 的相似性为潜在疫苗的研发带来了希望。我们分析了 EIAV 感染的宿主内模型，其中涉及抗体和细胞毒性 T 淋巴细胞（CTL）反应。在该模型中，具有长期抗体和 CTL 水平共存特征的生物学相关地方性平衡点的稳定性依赖于 CTL 和抗体增长率之间的平衡，这种平衡对于确保持续的 CTL 水平是必需的。我们确定了模型参数范围，在此范围内，CTL 和抗体的增殖率同时对系统走向共存的影响最大，并可以用来推导出 CTL 和抗体产生率之间的数学关系，以探索导致共存的分岔曲线。我们采用拉丁超立方抽样和最小二乘法来找到将地方性和边界平衡点均等划分的参数范围。然后，我们通过对参数进行局部敏感性分析来对该关系进行数值检验。我们的分析与先前的结果一致，即旨在通过两种免疫反应控制持续性病毒感染的干预措施（如疫苗）应适度控制抗体反应，以刺激 CTL 反应。最后，我们表明无论其他参数的影响如何，CTL 的产生率都可以完全决定长期结果，并根据所有模型参数的确定范围来提供产生此结果的条件。
