Abstract

Viruses are responsible of illness. The purpose of drug therapy is to fight bacterial infection and to achieve definite outcomes that improve the patient’s quality of life. Mathematical models combined with clinical studies can be useful in forecasting infection and understanding viral infections mechanism among host cells. In this work, incorporating stochastic fluctuations, we consider a viral infection model to describe the role of lytic and nonlytic immune responses. Lytic immunity is defined as the destruction of infected cells. Nonlytic immunity is defined as the inhibition of viral replication by soluble mediators secreted by immune cells. Mainly, we investigate near optimal control for drug therapy. We show sufficient and necessary conditions for the near optimality. Then, by means of adjoint equations, we estimate the error bound for the near optimality. Numerical illustrations indicate that the antiviral drug therapy may induce a significant decrease of the peaks of infected cells and free virions.

摘要

病毒是疾病的罪魁祸首。药物治疗的目的是对抗细菌感染并达到改善患者生活质量的明确结果。结合临床研究的数学模型可用于预测感染和了解宿主细胞之间的病毒感染机制。在这项工作中，结合随机波动，我们考虑了一种病毒感染模型来描述溶解性和非溶解性免疫反应的作用。裂解免疫被定义为感染细胞的破坏。非溶解性免疫被定义为免疫细胞分泌的可溶性介质抑制病毒复制。我们主要研究药物治疗的接近最佳控制。我们展示了接近最优的充分必要条件。然后，通过伴随方程，我们估计接近最优的误差界限。数字说明表明，抗病毒药物治疗可能会导致感染细胞和游离病毒粒子的峰值显着下降。