Research article Special Issues

Dynamics of a dengue disease transmission model with two-stage structure in the human population

  • Received: 26 July 2022 Revised: 19 September 2022 Accepted: 27 September 2022 Published: 20 October 2022
  • Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.

    Citation: Alian Li-Martín, Ramón Reyes-Carreto, Cruz Vargas-De-León. Dynamics of a dengue disease transmission model with two-stage structure in the human population[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 955-974. doi: 10.3934/mbe.2023044

    Related Papers:

  • Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.



    加载中


    [1] Dengue and severe dengue, OMS, 2022. Available from: https://www.who.int/news-room/fact-sheets/detail/dengue-and-severe-dengue
    [2] L. Esteva, C. Vargas, Analysis of a dengue disease transmission model, Math. Biosci., 150 (1998), 131–151. https://doi.org/10.1016/S0025-5564(98)10003-2 doi: 10.1016/S0025-5564(98)10003-2
    [3] L. Esteva, C. Vargas, Influence of vertical and mechanical transmission on the dynamics of dengue disease, Math. Biosci., 167 (2000), 51–64. https://doi.org/10.1016/S0025-5564(00)00024-9 doi: 10.1016/S0025-5564(00)00024-9
    [4] S. M. Garba, A. B. Gummel, M. A. Bakar, Backward bifurcations in dengue transmission dynamics. Math. Biosci., 215 (2008), 11–25. https://doi.org/10.1016/j.mbs.2008.05.002
    [5] I. Ghosh, P. K. Tiwari, J. Chattopadhyay, Effect of active case finding on dengue control: Implications from a mathematical model, J. Theor. Biol., 464 (2019), 50–62. https://doi.org/10.1016/j.jtbi.2018.12.027 doi: 10.1016/j.jtbi.2018.12.027
    [6] M. Andraud, N. Hens, C. Marais, P. Beutels, Dynamic epidemiological models for dengue transmission: A systematic review of structural approaches, PloS One, 7 (2012), e49085. https://doi.org/10.1371/journal.pone.0049085 doi: 10.1371/journal.pone.0049085
    [7] A. Abidemi, M. I. Abd Aziz, R. Ahmad, Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation, Chaos Soliton. Fract., 133 (2020), 109648. https://doi.org/10.1016/j.chaos.2020.109648 doi: 10.1016/j.chaos.2020.109648
    [8] A. Abidemi, H. O. Fatoyinbo, J. K. K. Asamoah, S. S. Muni, Analysis of dengue fever transmission dynamics with multiple controls: A mathematical approach, in 2020 International Conference on Decision Aid Sciences and Application (DASA), IEEE, (2020), 971–978. https://doi.org/10.1109/DASA51403.2020.9317064
    [9] J. K. K. Asamoah, E. Yankson, E. Okyere, G. Q. Sun, Z. Jin, R. Jan, Optimal control and cost-effectiveness analysis for dengue fever model with asymptomatic and partial immune individuals, Results Phys., 31 (2021), 104919. https://doi.org/10.1016/j.rinp.2021.104919 doi: 10.1016/j.rinp.2021.104919
    [10] A. Abidemi, J. Ackora-Prah, H. O. Fatoyinbo, J. K. K. Asamoah, Lyapunov stability analysis and optimization measures for a dengue disease transmission model, Phys. A Statist. Mechan. Appl., 602 (2022), 127646. https://doi.org/10.1016/j.physa.2022.127646 doi: 10.1016/j.physa.2022.127646
    [11] A. Abidemi, H. O. Fatoyinbo, J. K. K. Asamoah, S. S. Muni, Evaluation of the Efficacy of Wolbachia Intervention on Dengue Burden in a Population: A Mathematical Insight, in 2022 International Conference on Decision Aid Sciences and Applications (DASA), IEEE, (2022), 1618–1627. https://doi.org/DASA54658.2022.9765106
    [12] J. B. Siqueira Jr., C. M. T. Martinelli, G. E. Coelho, A. C. da Rocha Simplico, D. L. Hatch, Dengue and dengue hemorrhagic fever, Brazil, 1981–2002, Emerg. Infect. Dis., 11 (2005), 48. https://doi.org/10.3201/eid1101.031091 doi: 10.3201/eid1101.031091
    [13] R. Huy, P. Buchy, C. Ngan, S. Ong, R. Ali, S. Vong, et al., National dengue surveillance in Cambodia 1980–2008: Epidemiological and virological trends and the impact of vector control, Bull. World Health Organ., 88 (2010), 650–657. https://doi.org/10.2471/BLT.09.073908 doi: 10.2471/BLT.09.073908
    [14] S. Nimmannitya, S. Udomsakdi, J. E. Scanlon, P. Umpaivit, Dengue and chikungunya virus infection in man in Thailand, 1962–1964: IV. Epidemiological studies in the Bangkok metropolitan area, Am. J. Trop. Med. Hyg., 186 (1969), 997–1021. https://doi.org/10.4269/ajtmh.1969.18.997 doi: 10.4269/ajtmh.1969.18.997
    [15] S. Kongsomboon, P. Singhasivanon, J. Kaewkungwal, S. Nimmannitya, J. M. MP, A. Nisalak, et al., Temporal trends of dengue fever/dengue hemorrhagic fever un Bangkok, Thailand from 1981 to 2000: An age-period-cohort analysis, Age, 15 (2004), 0–15.
    [16] S. B. Halstead, More dengue, more questions. Emerg. Infect. Dis., 11 (2005), 740. https://doi.org/10.3201/eid1105.050346
    [17] K. T. D. Thai, N. Nagelkerke, H. L. Phuong, T. T. T. Nga, P. T. Giao, L. Q. Hung, et al., Geographical heterogeneity of dengue transmission in two villages in southern Vietnam, Epidemiol. Infect., 138 (2010), 585–591. https://doi.org/10.1017/S095026880999046X doi: 10.1017/S095026880999046X
    [18] E. E. Ooi, K. T. Goh, D. J. Gubler, Dengue prevention and 35 years of vector control in Singapore. Emerg. Infect. Dis., 12 (2006), 887. https://doi.org/10.3201/10.3201/eid1206.051210
    [19] A. K. Teng, S. Singh, Epidemiology and new initiatives in the prevention and control of dengue in Malaysia. WHO Regional Office for South-East Asia, Dengue Bull., 25 (2001), 7–14. https://apps.who.int/iris/handle/10665/163699
    [20] M. T. Alera, A. Srikiatkhachorn, J. M. Velasco, I. A. Tac-An, C. B. Lago, H. E. Clapham, et al., Incidence of dengue virus infection in adults and children in a prospective longitudinal cohort in the Philippines, PLoS Negl. Trop. Dis., 10 (2016), e0004337. https://doi.org/10.1371/journal.pntd.0004337 doi: 10.1371/journal.pntd.0004337
    [21] D. Aldila, T. Götz, E. Soewono, An optimal control problem arising from a dengue disease transmission model, Math. Biosci., 242 (2013), 9–16. https://doi.org/10.1016/j.mbs.2012.11.014 doi: 10.1016/j.mbs.2012.11.014
    [22] A. K. Supriatna, E. Soewono, S. A. van Gils, A two-age-classes dengue transmission model. Math. Biosci., 216 (2008), 114–121. https://doi.org/10.1016/j.mbs.2008.08.011
    [23] A. Chamnan, P. Pongsumpun, I. M. Tang, N. Wongvanich, Effect of a vaccination against the dengue fever epidemic in an age structure population: From the perspective of the local and global stability analysis, Mathematics, 10 (2022), 904. https://doi.org/10.3390/math10060904 doi: 10.3390/math10060904
    [24] L. Anderko, S. Chalupka, M. Du, M. Hauptman, Climate changes reproductive and children's health: A review of risks, exposures, and impacts, Pediatr. Res., 87 (2020), 414–419. https://doi.org/10.1038/s41390-019-0654-7 doi: 10.1038/s41390-019-0654-7
    [25] 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. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
    [26] C. W. Castillo-Garsow, C. Castillo-Chavez, A tour of the basic reproductive number and the next generation of researchers, in An Introduction to Undergraduate Research in Computational and Mathematical Biology (eds. H. C. Highlander, A. Capaldi and C. D. Eatonand), Springer, (2020), 87–124. https://doi.org/10.1007/978-3-030-33645-5-2
    [27] V. Lakshmikantham, S. Leela, A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York, 1989. https://doi.org/10.1002/asna.2103160113
    [28] L. Esteva, C. Vargas, C. Vargas-De-León, The role of asymptomatics and dogs on leishmaniasis propagation, Math. Biosci., 293 (2017), 46–55. https://doi.org/10.1016/j.mbs.2017.08.006 doi: 10.1016/j.mbs.2017.08.006
    [29] A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. Biol., 21 (2004), 75–83. https://doi.org/10.1093/imammb/21.2.75 doi: 10.1093/imammb/21.2.75
    [30] A. Korobeinikov, Global properties of basic virus dynamics models. Bull. Math. Biol., 66 (2004), 879–883. https://doi.org/10.1016/j.bulm.2004.02.001
    [31] C. Vargas-De-León, J. A. Castro-Hernández, Local and global stability of host–vector disease models, Foro-Red-Mat Revista Electrónica de Contenido Matemático, 25 (2008), 1–9. http://www.red-mat.unam.mx/foro/volumenes/vol025
    [32] C. Vargas-De-León, Global analysis of a delayed vector–bias Model for malaria transmission with incubation period in mosquitoes, Math. Biosci. Eng., 9 (2012), 165–174. https://doi.org/10.3934/mbe.2012.9.165 doi: 10.3934/mbe.2012.9.165
    [33] J. La Salle, S. Lefschetz, Stability by Liapunov's Direct Method with Applications, Academic Press, New York, 1961.
    [34] R. Elling, P. Henneke, C. Hatz, M. Hufnagel, Dengue fever in children: Where are we now, Pediatr. Infect. Dis. J., 32 (2013), 1020–1022. https://doi.org/10.1097/INF.0b013e31829fd0e9 doi: 10.1097/INF.0b013e31829fd0e9
    [35] B. Bounomo, R. Della Marca, Optimal bed net use for a dengue model with mosquito seasonal pattern, Math. Method. Appl. Sci., 41 (2018), 573–592. https://doi.org/10.1002/mma.4629 doi: 10.1002/mma.4629
    [36] M. Z. Ndii, N. Anggriani, J. J. Messakh, S. B. Djahi, Estimating the reproduction number and designing the integrated strategies against dengue., Results Phys., 27 (2021), 104473. https://doi.org/10.1016/j.rinp.2021.104473 doi: 10.1016/j.rinp.2021.104473
    [37] ODE Solvers, DifferentialEquations.jl, Avalible from: https://diffeq.sciml.ai/stable/solvers/ode_solve/
    [38] G. Chowell, C. Castillo-Chavez, P. W. Fenimore, C. M. Kribs-Zaleta, L. Arriola, J. M. Hyman, Model parameters and outbreak control for SARS, Emerg. Infect. Dis. J., 28 (2016). https://doi.org/10.3201/eid1007.030647
    [39] B. Troost, J. M. Smit, Recent advances in antiviral drug development towards dengue virus, Curr. Opin. Virol., 43 (2020), 9–21. https://doi.org/10.1016/j.coviro.2020.07.009 doi: 10.1016/j.coviro.2020.07.009
    [40] E. P. Lima, M. O. F. Goulart, M. L. R. Neto, Meta-analysis of studies on chemical, physical and biological agents in the control of Aedes aegypti, BMC Public Health, 15 (2015), 1–14. https://doi.org/10.1186/s12889-015-2199-y doi: 10.1186/s12889-015-2199-y
    [41] A. E. Bardach, H. A. García‐Perdomo, A. Alcaraz, E. Tapia Lopez, R. A. R. Gándara, S. Ruvinsky, et al., Interventions for the control of Aedes aegypti in Latin America and the Caribbean: Systematic review and meta-analysis, Trop. Med. Int. Health, 24 (2019), 530–552. https://doi.org/10.1111/tmi.13217 doi: 10.1111/tmi.13217
  • Reader Comments
  • © 2023 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2021) PDF downloads(230) Cited by(8)

Article outline

Figures and Tables

Figures(4)  /  Tables(1)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog