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

Yuyi Xue; Yanni Xiao; Yuyi Xue; Yanni Xiao

doi:10.3934/mbe.2020350

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6720-6736. doi: 10.3934/mbe.2020350

Previous Article Next Article

Research article Special Issues

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

Yuyi Xue ,
Yanni Xiao ^,

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

Received: 31 May 2020 Accepted: 16 September 2020 Published: 30 September 2020

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.
- 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[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6720-6736. doi: 10.3934/mbe.2020350

Related Papers:

Abstract

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.

References

[1]	R. M. Anderson, R. M. May, O. U. P. (OUP), Infectious diseases of human: dynamics and control, 1992.
[2]	O. Diekmann, J. Heesterbeek, Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation, Wiley Series in Mathematical and Computational Biology, Chichester, Wiley.
[3]	A. S. Perelson, P. W. Nelson, Mathematical Analysis Of HIV-1 Dynamics In Vivo, Siam. Rev., 41 (1999), 3-44. doi: 10.1137/S0036144598335107
[4]	P. Song, Y. Lou, Y. Xiao, A spatial seirs reaction-diffusion model in heterogeneous environment, J. Differ. Equations, 267 (2019), 5084-5114. doi: 10.1016/j.jde.2019.05.022
[5]	S. Wain-Hobson, Virus dynamics: Mathematical principles of immunology and virology, Nat. Med., 410 (2001), 412-413.
[6]	L. J. Abu-Raddad, R. V. Barnabas, H. Janes, H. A. Weiss, J. G. Kublin, I. M. Longini, et al., Have the explosive HIV epidemics in sub-Saharan Africa been driven by higher community viral load?, AIDS, 27 (2013), 2494-2496.
[7]	D. Wilson, M. Law, A. E. Grulich, D. A. Cooper, J. M. Kaldor, Relation between HIV viral load and infectiousness: a model-based analysis, The Lancet, 372 (2008), 314-320. doi: 10.1016/S0140-6736(08)61115-0
[8]	T. C. Quinn, M. J. Wawer, N. Sewankambo, D. Serwadda, R. H. Gray, Viral load and heterosexual transmission of human immunodeficiency virus type 1, New. Engl. J. Med., 342 (2000), 921-929. doi: 10.1056/NEJM200003303421303
[9]	L. M. Childs, F. E. Moustaid, Z. Gajewski, S. Kadelka, R. Nikinbeers, J. W. Smith, et al., Linked within-host and between-host models and data for infectious diseases: a systematic review, PeerJ, 7 (2019), e7057.
[10]	N. Dorratoltaj, R. Nikinbeers, S. M. Ciupe, S. Eubank, K. Abbas, Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models, PeerJ, 5 (2017), e3877.
[11]	A. Gandolfi, A. Pugliese, C. Sinisgalli, Epidemic dynamics and host immune response: a nested approach, J. Math. Biol., 70 (2015), 399-435. doi: 10.1007/s00285-014-0769-8
[12]	W. Garira, A primer on multiscale modelling of infectious disease systems, Infect. Dis. Model., 3 (2018), 176-191.
[13]	W. Garira, A complete categorization of multiscale models of infectious disease systems, J. Biol. Dyn., 11 (2017), 378-435. doi: 10.1080/17513758.2017.1367849
[14]	M. A. Gilchrist, D. Coombs, Evolution of virulence: Interdependence, constraints, and selection using nested models, Theor. Popul. Biol., 69 (2006), 145-153.
[15]	M. Park, C. Loverdo, S. J. Schreiber, J. O. Lloydsmith, Multiple scales of selection influence the evolutionary emergence of novel pathogens, Philos. T. R. Soc. B., 368 (2013), 20120333. doi: 10.1098/rstb.2012.0333
[16]	M. Shen, Y. Xiao, L. Rong, Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics, Math. Biosci., 263 (2015), 37-50. doi: 10.1016/j.mbs.2015.02.003
[17]	M. Shen, Y. Xiao, L. Rong, L. A. Meyers, Conflict and accord of optimal treatment strategies for HIV infection within and between hosts, Math. Biosci., 309 (2019), 107-117. doi: 10.1016/j.mbs.2019.01.007
[18]	M. Shen, Y. Xiao, L. Rong, G. Zhuang, Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model, Appl. Math. Model., 75 (2019), 162-200. doi: 10.1016/j.apm.2019.05.024
[19]	Z. Feng, X. Cen, Y. Zhao, J. Velasco-Hernandez, Coupled within-host and between-host dynamics and evolution of virulence, Math. Biosci., 270 (2015), 204-212.
[20]	Z. Feng, J. Velasco-Hernandez, B. Tapia-Santos, A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease, Math. Biosci., 241 (2013), 49-55.
[21]	X. Wang, S. Tang, A multiscale model on hospital infections coupling macro and micro dynamics, Commun. Nonlinear. Sci., 50 (2017), 256-270. doi: 10.1016/j.cnsns.2017.03.009
[22]	X. Sun, Y. Xiao, Multiscale system for environmentally-driven infectious disease with threshold control strategy, Int. J. Bifurcat. Chaos, 28 (2018), 1850064. doi: 10.1142/S0218127418500645
[23]	Y. Xiao, C. Xiang, R. Cheke, S. Tang, Coupling the macroscale to the microscale in a spatiotemporal context to examine effects of spatial diffusion on disease transmission, B. Math. Biol., 82 (2020), 1-27. doi: 10.1007/s11538-019-00680-3
[24]	S. Bhattacharya, M. Martcheva, An immuno-eco-epidemiological model of competition, J. Biol. Dyn., 10 (2016), 314-341. doi: 10.1080/17513758.2016.1186291
[25]	T. Kostova, Persistence of viral infections on the population level explained by an immunoepidemiological model, Math. Biosci., 206 (2007), 309-319. doi: 10.1016/j.mbs.2005.08.003
[26]	E. C. Manda, F. Chirove, Modelling coupled within host and population dynamics of and HIV infection, J. Math. Biol., 76 (2018), 1123-1158. doi: 10.1007/s00285-017-1170-1
[27]	X. Cen, Z. Feng, Y. Zhao, Emerging disease dynamics in a model coupling within-host and between-host systems, J. Theor. Biol., 361 (2014), 141-151. doi: 10.1016/j.jtbi.2014.07.030
[28]	B. Boldin, O. Diekmann, Superinfections can induce evolutionarily stable coexistence of pathogens, J. Math. Biol., 56 (2008), 635-672. doi: 10.1007/s00285-007-0135-1
[29]	P. Dreessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)