Mathematical modeling and analysis of innate and humoral immune responses to dengue infections

Abstract

Dengue is an acute arthropode-borne virus, belonging to the family Flaviviridae. Currently, there are no vaccines or treatments available against dengue. Thus it is important to understand the dynamics of dengue in order to control the infection. In this paper, we study the long-term dynamics of the model that is presented in [S. D. Perera and S. S. N. Perera, Simulation model for dynamics of dengue with innate and humoral immune responses, Comput. Math. Methods Med. 2018 (2018) 8798057, 18 pp. https://doi.org/10.1155/2018/8798057 ] which describes the interaction of virus with infected and uninfected cells in the presence of innate and humoral immune responses. It was found the model has three equilibria, namely: infection free equilibrium, no immune equilibrium and endemic equilibrium, then analyzed its stability analytically. The analytical findings of each model have been exemplified by numerical simulations. Given the fact that intensity of dengue virus replication at early times of infection could determine clinical outcomes, it is important to understand the impact of innate immunity, which is believed to be the first line of defense against an invading pathogen. For this we carry out a simulation case study to investigate the importance of innate immune response on dengue virus dynamics. A comparison was done assuming that innate immunity was active; innate immunity was in quasi-steady state and innate immunity was inactive during the virus replication process. By a further analysis of the qualitative behavior of the quasi-steady state, it was observed that innate immune response plays a pivotal role in dengue virus dynamics. It can change the dynamical behavior of the system and is essential for the virus clearance.