Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|Number of page(s)||13|
|Published online||26 March 2019|
Immune response in HIV epidemics for distinct transmission rates and for saturated CTL response
Faculty of Sciences, University of Porto,
Rua do Campo Alegre s/n,
2 School of Engineering, Polytechnic of Porto, Center for Mathematics of the University of Porto, Rua Dr António Bernardino de Almeida 431, 4249-015 Porto, Portugal.
* Corresponding author: firstname.lastname@example.org
Accepted: 5 February 2019
In this paper, we study the immune response in a fractional order model for HIV dynamics, for distinct disease transmission rates and saturated cytotoxic T-lymphocyte (CTL) response. Our goal is twofold: (i) to analyze the role of the order of the fractional derivative, α, on the efficacy of the immune response, (ii) to examine the immune response for distinct transmission functions, in the presence of saturated CTL response. We compute the reproduction number of the model and state the stability of the disease-free equilibrium. We discuss the results of the model from an epidemiological point of view.
Mathematics Subject Classification: 34A08 / 34A34 / 92C60
Key words: HIV infection / disease transmission rates / saturated CTL response / fractional model
© EDP Sciences, 2019
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