Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission by Priti Kumar Roy

Author:Priti Kumar Roy
Language: eng
Format: epub, pdf
Publisher: Springer Singapore, Singapore

© Springer Science+Business Media Singapore 2015

Priti Kumar RoyMathematical Models for Therapeutic Approaches to Control HIV Disease TransmissionIndustrial and Applied Mathematics10.1007/978-981-287-852-6_5

5. Insight of Delay Dynamics

Priti Kumar Roy1

(1)Department of Mathematics, Jadavpur University, Kolkata, India

Priti Kumar Roy

Email: [email protected]

Abstract

Delay effects during long-term HIV infection have been studied extensively. Here we have considered a time delay in the process of infection in the healthy T cells. Furthermore, we have also included a similar delay in the killing rate of infected CD4 T cells by Cytotoxic T-Lymphocytes (CTLs) and in the stimulation of CTLs. Since the process of generation of CTLs is not instantaneous, we have assimilated a realistic time lag in the production term of CTLs in our basic mathematical model of the HIV-1 infection. We have estimated the length of delay for which the stability of the system remains preserved. We have obtained the threshold value for delay parameter, below this critical value, interior equilibrium point becomes asymptotically stable. When the value of this delay parameter exceeds this threshold value, interior equilibrium point becomes unstable and a Hopf bifurcation occurs.

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