A delay-dependent model with HIV drug resistance during therapy |
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Authors: | Yan Wang Fred Brauer Jianhong Wu Jane M Heffernan |
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Institution: | 1. College of Science, China University of Petroleum, Qingdao, Shandong 266580, China;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;3. Centre for Disease Modelling, York Institute for Health Research, Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada |
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Abstract: | The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density. |
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Keywords: | HIV Drug resistance Antiretroviral therapy Intracellular delay Asymptotic stability Hopf bifurcation |
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