Estimation of the HIV-1 infection rate and the basic reproductive ratio

• Published in: Computational & applied mathematics Vol. 37; no. 3; pp. 3267 - 3282
• Main Authors: Bobko, Nara, Zubelli, Jorge Passamani
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Computer simulation; HIV; Human immunodeficiency virus; Immune system; Infections; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical models; Mathematics; Mathematics and Statistics; Parameter estimation; Patients; Basic reproductive ratio; Global stability; HIV-1 dynamics; Primary 92C50; Secondary 34D23; Parameters’ estimation; Infection rate
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-017-0500-7

This paper proposes and analyzes an alternative method to estimate important parameters of the HIV-1 infection: the infection rate and the basic reproductive ratio (in the presence and absence of the immune response). These parameters are of great relevance, impacting on the infection chronicity. The method consists in comparing clinical data in the chronic stage with predicted equilibrium points of a mathematical model which describes the dynamics of HIV-1 in the acute infection phase. The fact that the method uses only clinical data relating to the chronic stage is an important aspect since most patients are diagnosed at this stage, and thus only have data available for this stage. A comparison between the proposed method and other estimation methods, as well as between numerical simulations, is presented and the results are quite satisfactory. In addition, by applying the proposed method for data of 31 patients, we estimate the basic reproductive ratio in the presence of the immune response and the HIV-1 infection rate for which we obtained a median of 1.95 (IQR 0.55) and 1.96 × 10 - 5 mm 3 virions - 1 day - 1 (IQR 3.52 × 10 - 5 ), respectively.