Prevention and control of Ebola virus transmission: mathematical modelling and data fitting. (English) Zbl 07893160
Summary: The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D30 | Epidemiology |
| 34K21 | Stationary solutions of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
Ebola virus disease; environmental transmission; time-varying reproduction number; effective reproduction number; inoculation ratio; data fittingReferences:
| [1] | Al-Darabsah, I.; Yuan, Y., A time-delayed epidemic model for Ebola disease transmission, Appl Math Comput, 290, 307-325, 2016 · Zbl 1410.92115 |
| [2] | Aruna, A.; Mbala, P.; Minikulu, L., Ebola virus disease outbreak-democratic republic of the Congo, August 2018-November 2019, MMWR Morb Mortal Wkly Rep, 68, 50, 1162, 2019 · doi:10.15585/mmwr.mm6850a3 |
| [3] | Bai, N.; Song, C.; Xu, R., Mathematical analysis and application of a cholera transmission model with waning vaccine-induced immunity, Nonlinear Anal: RWA, 58, 103, 232, 2021 · Zbl 1453.92288 |
| [4] | Bani-Yaghoub, M.; Gautam, R.; Shuai, Z., Reproduction numbers for infections with free-living pathogens growing in the environment, J Biol Dyn, 6, 2, 923-940, 2012 · Zbl 1447.92395 · doi:10.1080/17513758.2012.693206 |
| [5] | Berge, T.; Lubuma, JS; Moremedi, GM, A simple mathematical model for Ebola in Africa, J Biol Dyn, 11, 1, 42-74, 2017 · Zbl 1448.92276 · doi:10.1080/17513758.2016.1229817 |
| [6] | Berge, T.; Bowong, S.; Lubuma, J., Modeling Ebola virus disease transmissions with reservoir in a complex virus life ecology, Math Biosci Eng, 15, 1, 21-56, 2018 · Zbl 1378.34071 · doi:10.3934/mbe.2018002 |
| [7] | Bodine, EN; Cook, C.; Shorten, M., The potential impact of a prophylactic vaccine for Ebola in Sierra Leone, Math Biosci Eng, 15, 2, 337-359, 2018 · Zbl 1375.92062 · doi:10.3934/mbe.2018015 |
| [8] | Browne, CJ; Gulbudak, H.; Macdonald, JC, Differential impacts of contact tracing and lockdowns on outbreak size in COVID-19 model applied to China, J Theor Biol, 532, 110, 919, 2022 · Zbl 1476.92040 |
| [9] | Buonomo, B.; Della Marca, R.; d’Onofrio, A., A behavioural modelling approach to assess the impact of COVID-19 vaccine hesitancy, J Theor Biol, 534, 110, 973, 2022 · Zbl 1480.92123 |
| [10] | Caleo, G.; Duncombe, J.; Jephcott, F., The factors affecting household transmission dynamics and community compliance with Ebola control measures: a mixed-methods study in a rural village in Sierra Leone, BMC Public Health, 18, 1, 1-13, 2018 · doi:10.1186/s12889-018-5158-6 |
| [11] | Castillo-Chevez C, Thieme HR (1995) Asymptotically autonomous epidemic models. In: Mathematical Population Dynamics: Analysis of Heterogeneity, vol. 1. Theory of Epidemics |
| [12] | CDC (2021) Signs and symptoms. https://www.cdc.gov/vhf/ebola/symptoms/index.html |
| [13] | Choi, MJ; Cossaboom, CM; Whitesell, AN, Use of Ebola vaccine: recommendations of the advisory committee on immunization practices, United States, 2020, MMWR Recomm Rep, 70, 1, 1-12, 2021 · doi:10.15585/mmwr.rr7001a1 |
| [14] | Codeço, CT, Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir, BMC Infect Dis, 1, 1, 1-14, 2001 · doi:10.1186/1471-2334-1-1 |
| [15] | Dénes, A.; Gumel, AB, Modeling the impact of quarantine during an outbreak of Ebola virus disease, Infect Dis Model, 4, 12-27, 2019 |
| [16] | Deng, J.; Tang, S.; Shu, H., Joint impacts of media, vaccination and treatment on an epidemic Filippov model with application to COVID-19, J Theor Biol, 532, 110, 698, 2021 · Zbl 1466.92177 |
| [17] | Hale, JK, Theory of functional differential equation, 1977, New York: Springer, New York · Zbl 0352.34001 · doi:10.1007/978-1-4612-9892-2 |
| [18] | Hasan, S.; Ahmed, SA; Masood, R., Ebola virus: a global public health menace: a narrative review, J Fam Med Prim Care, 8, 7, 2189-2201, 2019 · doi:10.4103/jfmpc.jfmpc_297_19 |
| [19] | Hossain, L.; Kam, D.; Kong, F., Social media in Ebola outbreak, Epidemiol Infect, 144, 10, 2136-2143, 2016 · doi:10.1017/S095026881600039X |
| [20] | Househ, M., Communicating Ebola through social media and electronic news media outlets: a cross-sectional study, Health Inform J, 22, 3, 470-478, 2016 · doi:10.1177/1460458214568037 |
| [21] | Hunt, AG, Exponential growth in Ebola outbreak since May 14, 2014, Complexity, 20, 2, 8-11, 2014 · doi:10.1002/cplx.21615 |
| [22] | Jacob, ST; Crozier, I.; Fischer, WA, Ebola virus disease, Nat Rev Dis Primers, 6, 13, 2020 · doi:10.1038/s41572-020-0147-3 |
| [23] | Jacobsen, KH; Aguirre, AA; Bailey, CL, Lessons from the Ebola outbreak: action items for emerging infectious disease preparedness and response, EcoHealth, 13, 1, 200-212, 2016 · doi:10.1007/s10393-016-1100-5 |
| [24] | Kahn, R.; Peak, CM; Fernández-Gracia, J., Incubation periods impact the spatial predictability of cholera and Ebola outbreaks in Sierra Leone, Proc Natl Acad Sci USA, 117, 9, 5067-5073, 2020 · doi:10.1073/pnas.1913052117 |
| [25] | Kamorudeen, RT; Adedokun, KA; Olarinmoye, AO, Ebola outbreak in West Africa, 2014-2016: epidemic timeline, differential diagnoses, determining factors, and lessons for future response, J Infect Public Heal, 13, 7, 956-962, 2020 · doi:10.1016/j.jiph.2020.03.014 |
| [26] | Kawuki, J.; Musa, TH; Yu, X., Impact of recurrent outbreaks of Ebola virus disease in Africa: a meta-analysis of case fatality rates, Public Health, 195, 89-97, 2021 · doi:10.1016/j.puhe.2021.03.027 |
| [27] | Lawrence, P.; Danet, N.; Reynard, O., Human transmission of Ebola virus, Curr Opin Virol, 22, 51-58, 2017 · doi:10.1016/j.coviro.2016.11.013 |
| [28] | Liu, R.; Wu, J.; Zhu, H., Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput Math Methods Med, 8, 3, 153-164, 2007 · Zbl 1121.92060 · doi:10.1080/17486700701425870 |
| [29] | Marino, S.; Hogue, IB; Ray, CJ, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J Theor Biol, 254, 1, 178-196, 2008 · Zbl 1400.92013 · doi:10.1016/j.jtbi.2008.04.011 |
| [30] | Mukandavire, Z.; Liao, S.; Wang, J., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proc Natl Acad Sci USA, 108, 21, 8767-8772, 2011 · doi:10.1073/pnas.1019712108 |
| [31] | Nduka, UC; Igwe-Omoke, A.; Ogugua, C., The use of social media in combating the Ebola virus in Nigeria-a review, Int J Med Health Dev, 19, 1, 97-108, 2014 |
| [32] | Nicastri, E.; Kobinger, G.; Vairo, F., Ebola virus disease: epidemiology, clinical features, management, and prevention, Infect Dis Clin N Am, 33, 4, 953-976, 2019 · doi:10.1016/j.idc.2019.08.005 |
| [33] | Piercy, T.; Smither, S.; Steward, J., The survival of filoviruses in liquids, on solid substrates and in a dynamic aerosol, J Appl Microbiol, 109, 5, 1531-1539, 2010 |
| [34] | Rivers CM, Lofgren ET, Marathe M et al (2014) Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia. PLoS Curr 6. doi:10.1371/currents.outbreaks.4d41fe5d6c05e9df30ddce33c66d084c |
| [35] | Rojas, M.; Monsalve, DM; Pacheco, Y., Ebola virus disease: an emerging and re-emerging viral threat, J Autoimmun, 106, 102, 375, 2020 |
| [36] | Shen, M.; Xiao, Y.; Rong, L., Modeling the effect of comprehensive interventions on Ebola virus transmission, Sci Rep UK, 5, 1, 1-14, 2015 |
| [37] | Smith, HL, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, 1995, Providence: American Mathematical Society, Providence · Zbl 0821.34003 |
| [38] | Team, WER, West African Ebola epidemic after one year-slowing but not yet under control, New Engl J Med, 372, 6, 584-587, 2015 · doi:10.1056/NEJMc1414992 |
| [39] | Tomori, O.; Kolawole, MO, Ebola virus disease: current vaccine solutions, Curr Opin Immunol, 71, 27-33, 2021 · doi:10.1016/j.coi.2021.03.008 |
| [40] | Tsanou, B.; Bowong, S.; Lubuma, J., Assessing the impact of the environmental contamination on the transmission of Ebola virus disease (EVD), J Appl Math Comput, 55, 1, 205-243, 2017 · Zbl 1377.92101 · doi:10.1007/s12190-016-1033-8 |
| [41] | UN (2019) World population prospects 2019. https://population.un.org/wpp/Download/Standard/Population/ |
| [42] | UNMEER (2014) Sierra Leone: Ebola emergency weekly situation report no. 07. UNMEER, Sierra Leone |
| [43] | van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math Biosci, 180, 1-2, 29-48, 2002 · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6 |
| [44] | Vetter, P.; Fischer, WA; Schibler, M., Ebola virus shedding and transmission: review of current evidence, J Infect Dis, 214, suppl-3, S177-S184, 2016 · doi:10.1093/infdis/jiw254 |
| [45] | Walldorf, JA; Cloessner, EA; Hyde, TB, Considerations for use of Ebola vaccine during an emergency response, Vaccine, 37, 48, 7190-7200, 2019 · doi:10.1016/j.vaccine.2017.08.058 |
| [46] | WHO (2015) Who: Ebola situation report. https://apps.who.int/iris/discover?rpp=10 &etal=0 &query=Ebola &group_by=none &page=7 |
| [47] | WHO (2016) Ebola situation report-17 February 2016. https://apps.who.int/iris/discover?query=WHO+Ebola+Situation+Report+-+17+February+2016 |
| [48] | WHO (2021) Ebola virus disease. https://www.who.int/news-room/fact-sheets/detail/ebola-virus-disease |
| [49] | Xiao, YN; Zhou, YC; Tang, SY, Principle of biomathematics (in Chinese), 2012, Xi’an: Xi’an Jiaotong University Press, Xi’an |
| [50] | Xu, R.; Ma, Z., Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal: RWA, 10, 5, 3175-3189, 2009 · Zbl 1183.34131 · doi:10.1016/j.nonrwa.2008.10.013 |
| [51] | Yang, C.; Wang, J., A cholera transmission model incorporating the impact of medical resources, Math Biosci Eng, 16, 5, 5226-5246, 2019 · Zbl 1497.92319 · doi:10.3934/mbe.2019261 |
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