Impact of variability of reproductive ageing and rate on childhood infectious disease prevention and control: insights from stage-structured population models

Qiuyi Su; Jianhong Wu; Qiuyi Su; Jianhong Wu

doi:10.3934/mbe.2020390

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7671-7691. doi: 10.3934/mbe.2020390

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Impact of variability of reproductive ageing and rate on childhood infectious disease prevention and control: insights from stage-structured population models

Qiuyi Su ,
Jianhong Wu ^,

Laboratory for Industrial and Applied Mathematics (LIAM), Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

Received: 30 August 2020 Accepted: 28 October 2020 Published: 04 November 2020

We propose a stage-structured model of childhood infectious disease transmission dynamics, with the population demographics dynamics governed by a certain family and population planning strategy giving rise to nonlinear feedback delayed effects on the reproduction ageing and rate. We first describe the long-term aging-profile of the population by describing the pattern and stability of equilibrium of the demographic model. We also investigate the disease transmission dynamics, using the epidemic model when the population reaches the positive equilibrium (limiting equation). We establish conditions for the existence, uniqueness and global stability of the disease endemic equilibrium. We then prove the global stability of the endemic equilibrium for the original epidemic model with varying population demographics. The global stability of the endemic equilibrium allows us to examine the effects of reproduction ageing and rate, under different family planning strategies, on the childhood infectious disease transmission dynamics. We also examine demographic distribution, diseases reproductive number, infant disease rate and age distribution of disease, and as such, the work can be potentially used to inform targeted age group for optimal vaccine booster programs.
- childhood infectious diseases,
- stage structured dynamical model,
- delay differential equation,
- stability,
- nonlinear feedback on reproduction ageing and rate
Citation: Qiuyi Su, Jianhong Wu. Impact of variability of reproductive ageing and rate on childhood infectious disease prevention and control: insights from stage-structured population models[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7671-7691. doi: 10.3934/mbe.2020390

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Abstract

We propose a stage-structured model of childhood infectious disease transmission dynamics, with the population demographics dynamics governed by a certain family and population planning strategy giving rise to nonlinear feedback delayed effects on the reproduction ageing and rate. We first describe the long-term aging-profile of the population by describing the pattern and stability of equilibrium of the demographic model. We also investigate the disease transmission dynamics, using the epidemic model when the population reaches the positive equilibrium (limiting equation). We establish conditions for the existence, uniqueness and global stability of the disease endemic equilibrium. We then prove the global stability of the endemic equilibrium for the original epidemic model with varying population demographics. The global stability of the endemic equilibrium allows us to examine the effects of reproduction ageing and rate, under different family planning strategies, on the childhood infectious disease transmission dynamics. We also examine demographic distribution, diseases reproductive number, infant disease rate and age distribution of disease, and as such, the work can be potentially used to inform targeted age group for optimal vaccine booster programs.

References

[1]	G. Casey, O. Galor, Population and Demography Perspective Paper, Copenhagen Consensus Center, 2014.
[2]	S. Basten, Q. Jiang, Fertility in China: an uncertain future, Popul. Stud., 69 (2015), S97-S105.
[3]	Q. Ke, L. Zhang, C. He, Z. Zhao, M. Qi, R. C. Griggs, et al., China's shift from population control to population quality, Neurology, 87 (2016), e85-e88.
[4]	X. Yuan, The transformation and deduction of Chinese population, Chin. J. Popul. Sci., 01 (2000), 40-45.
[5]	SINA, Spokesperson of the one-child policy committee: 11% or more of the population may have two children, 2007. Available from: http://news.sina.com.cn/c/2007-07-10/154513416121.shtml.
[6]	China Daily, Most Chinese provincial areas relax one-child policy, 2014. Available from: http://www.chinadaily.com.cn/china/2014-07/10/content17706811.htm.
[7]	BBC, China to end one-child policy and allow two, 2018. Available from: https://www.bbc.com/news/world-asia-34665539.
[8]	D. Tang, The Times, China to scrap family planning rules as birthrate dwindles, 2018. Available from: https://www.thetimes.co.uk/article/china-to-scrap-family-planning-rulesas-birthrate-dwindles-x82kccgl3.
[9]	S. Li, C. Ma, L. Hao, Q. Su, Z. An, F. Ma, et al., Demographic transition and the dynamics of measles in six provinces in China: A modeling study, PLoS Med., 14 (2017), e1002255.
[10]	C. Connolly, R. Keil, S. H. Ali, Extended urbanisation and the spatialities of infectious disease: Demographic change, infrastructure and governance, Urban Stud., (2020), 1-19.
[11]	L. Gao, H. Hethcote, Simulations of rubella vaccination strategies in China, Math. Biosci., 202 (2006), 371-385. doi: 10.1016/j.mbs.2006.02.005
[12]	M. Iannelli, P. Manfredi, Demographic Change and Immigration in Agestructured Epidemic Models, Math. Popul. Stud., 14 (2007), 169-191. doi: 10.1080/08898480701426241
[13]	N. Geard, K. Glass, J. M. McCaw, E. S. McBryde, K. B. Korb, M. J. Keeling, et al., The effects of demographic change on disease transmission and vaccine impact in a household structured population, Math. Popul. Stud., 13 (2015), 56-64.
[14]	M. P. Dafilis, F. Frascoli, J. McVernon, J. M. Heffernan, J. M. McCaw, The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission, J. Theor. Biol., 361 (2014), 124-132.
[15]	S. A. McDonald, A. van Lier, D. Plass, M. EE Kretzschmar The impact of demographic change on the estimated future burden of infectious diseases: examples from hepatitis B and seasonal influenza in the Netherlands, BMC Public Health, 12 (2012), 1046. doi: 10.1186/1471-2458-12-1046
[16]	P. van den Driessche, 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
[17]	M. W. Hirsch, System of differential equations that are competitive or cooperative II: convergence almost everywhere, SIAM J. Math. Anal., 16 (1985), 423-439. doi: 10.1137/0516030
[18]	K. Mischaikov, H. Smith, H. R. Thieme, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Trans. Am. Math. Soc., 347 (1995), 1669-1685. doi: 10.1090/S0002-9947-1995-1290727-7

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