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Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Special Issues: Multiscale dynamics of infectious diseases, immune responses and therapeutics

There are many challenges to constitute the linkage from the macroscale to the microscale and analyze the multiscale model. We proposed a bidirectional coupling model with standard incidence which includes the interaction of between-host transmission dynamics and within-host viral dynamics, and investigated the dynamic behaviors of the multiscale system on two time-scales. We found that the multiscale system exhibits more complex dynamics including backward bifurcation, which means that the usual thresholds for infection control or virus elimination obtained from the epidemiological model or virus dynamic model may not act as threshold parameter under a certain condition. There may be multiple epidemic equilibriums, one of which is stable, although the basic reproduction number is less than 1. We numerically examine the synergistic impact between the macro and micro dynamics. In particular, increasing the drug efficacy can decrease the prevalence of disease. The contact rate may affect the number and size of equilibria of viral dynamics model by inducing the occurrence of backward bifurcation. The finding suggests that the effective control measures may include both the reduction in contact rate or transmission rate at the population level and the increase in drug efficacy at the individual level, and using these control measures together can effectively control the diseases.
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Keywords multiscale model; standard incidence; threshold dynamics; backward bifurcation

Citation: Yuyi Xue, Yanni Xiao. Analysis of a multiscale HIV-1 model coupling within-host viral dynamics and between-host transmission dynamics. Mathematical Biosciences and Engineering, 2020, 17(6): 6720-6736. doi: 10.3934/mbe.2020350

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