title: Role of active and inactive cytotoxic immune response in human immunodeficiency virus dynamics.
abstract: OBJECTIVE
  Mathematical models can be helpful to understand the complex dynamics of human immunodeficiency virus infection within a host. Most of work has studied the interactions of host responses and virus in the presence of active cytotoxic immune cells, which decay to zero when there is no virus. However, recent research highlights that cytotoxic immune cells can be inactive but never be depleted.
  
  
  METHODS
  We propose a mathematical model to investigate the human immunodeficiency virus dynamics in the presence of both active and inactive cytotoxic immune cells within a host. We explore the impact of the immune responses on the dynamics of human immunodeficiency virus infection under different disease stages.
  
  
  RESULTS
  Standard mathematical and numerical analyses are presented for this new model. Specifically, the basic reproduction number is computed and local and global stability analyses are discussed.
  
  
  CONCLUSIONS
  Our results can give helpful insights when designing more effective drug schedules in the presence of active and inactive immune responses.
authors: Licenciatura en Matemáticas, Universidad del Quindío, Quindío, Colombia.
authors: Hernan Dario
authors: HD
authors: Toro Zapata
authors: Departamento de Matematicas, Universidad del Valle, Cali, Colombia.
authors: Angelica Graciela
authors: AG
authors: Caicedo Casso
authors: Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ, USA.
authors: Derdei
authors: D
authors: Bichara
authors: Department of Applied Mathematics, Kyung Hee University, Yongin, Korea.
authors: Sunmi
authors: S
authors: Lee
keywords: Active immune response; Human immunodeficiency virus; Inactive immune response; Mathematical model