A latency fractional order model for HIV dynamics

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• 作者：Carla M.A. Pinto^a ; ^{cap@isep.ipp.pt" class="auth_mail" title="E-mail the corresponding author} ; Ana R.M. Carvalho^b ; ^{up200802541@fc.up.pt" class="auth_mail" title="E-mail the corresponding author}
• 关键词：HIV/AIDS ; HIV latency ; Fractional models
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：240-256
• 全文大小：1248 K

文摘

We study a fractional order model for HIV infection where latent T helper cells are included. We compute the reproduction number of the model and study the stability of the disease free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative 1-s2.0-S0377042716302539&_mathId=si2.gif&_user=111111111&_pii=S0377042716302539&_rdoc=1&_issn=03770427&md5=74c1652979b35a8bb44cbae3d86dadc9" title="Click to view the MathML source">α$\alpha$. In terms of epidemics, this suggests that varying 1-s2.0-S0377042716302539&_mathId=si2.gif&_user=111111111&_pii=S0377042716302539&_rdoc=1&_issn=03770427&md5=74c1652979b35a8bb44cbae3d86dadc9" title="Click to view the MathML source">α$\alpha$ induces a change in the patients’ epidemic status. Moreover, we simulate the variation of relevant parameters, such as the fraction of uninfected CD41" class="mathmlsrc">1-s2.0-S0377042716302539&_mathId=si71.gif&_user=111111111&_pii=S0377042716302539&_rdoc=1&_issn=03770427&md5=e74e1bbfe1e5c95b753e569bba39369c" title="Click to view the MathML source">⁺ T cells that become latently infected, and the CTLs proliferation rate due to infected CD41" class="mathmlsrc">1-s2.0-S0377042716302539&_mathId=si71.gif&_user=111111111&_pii=S0377042716302539&_rdoc=1&_issn=03770427&md5=e74e1bbfe1e5c95b753e569bba39369c" title="Click to view the MathML source">⁺ T cells. The model produces biologically reasonable results.