Viral dynamics of an HIV model with pulse antiretroviral therapy and adherence

Yang, Youping ¹

¹ School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. China

Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 516-528.

Résumé

An immunological model of HIV-1 infection that accounts for antiretroviral drug uptake via explicit compartments is considered. Different from traditional methods where the drug effects is modeled implicitly as a proportional inhibition of viral infection and production, in this paper, it is assumed that the CD4$^+$ T cells can 'prey on' the antiretroviral drugs and become the cells which cannot be infected or produce new virions. Drug dymamics is modeled applying impulsive differential equations. The basic reproductive number $R_0$ is defined via the next infection operator. It is shown that with perfect adherence the virus can be eradicated permanently if $R_0$ is less than unity, otherwise, the virus can persist by applying persistent theory. The effects of imperfect adherence are also explored. The results indicate that even for the same degree of adherence, different adherence patterns may lead to different therapy outcomes. In particular, for regular dosage missing, the more dosages are consecutively missed, the worse therapy outcomes will be.

Détail

DOI : 10.22436/jnsa.011.04.08

Classification : 34C60, 37C75, 92B05
Keywords: Impulsive therapy, imperfect adherence, basic reproductive number, adherence pattern

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