A study of a stochastic model and extinction phenomenon of meningitis epidemic
-
Samaila Jackson Yaga
und
Funmilayo W.O. Saporu
Abstract
Objectives
A stochastic version of the deterministic model for meningitis epidemic by Yaga and Saporu (A study of a deterministic model for meningitis epidemic. J Epidemiol Methods 2024;13:20230023) is developed.
Method
The stochastic mean system of equations for possible state of an individual in the model and the extinction probabilities for carrier and infective are derived. Comparison of the system of stochastic mean equations and its deterministic analogue of profiles for the various compartments and the case-carrier trajectories show similar pattern with a time shift difference.
Results
This indicates that there must be caution in using the deterministic analogue as an approximating system of the stochastic mean equations for inferential purpose. Simulation studies of the comparison of the compartmental profiles for the general case; model I, with the assumption that a proportion (φ≠0), of the infected susceptible can move directly to the infective stage and that of the special case, model II, when φ=0 is examined for various values of ϵ (odds in favour of a carrier transmitting infection)
Conclusion
It is concluded that carriership play a more prominent role in the transmission of meningitis epidemic and efforts aimed at control should be targeted at reducing the transmission rate and increasing the loss of carriership.
-
Author contributions: All authors participated in the production of the manuscript from beginning to the end.
-
Research ethics: Not applicable.
-
Informed consent: Not applicable.
-
Use of Large Language Models, AI and Machine Learning Tools: None declared.
-
Conflict of interest: The authors state no conflict of interest.
-
Research funding: None declared.
-
Data availability: Not applicable.
References
1. WHO. Meningitis. 2021 [Online]. https://www.who.int/news-room/fact-sheets/detail/meningitis [Accessed 28 Sept 2021].Suche in Google Scholar
2. Meyer, SA, Kristiansen, PA. Household transmission of neisseria meningitidis in the meningitis belt. Lancet Glob Health 2016;4:e885–6.37. https://doi.org/10.1016/s2214-109x(16)30292-3.Suche in Google Scholar
3. Stephens, DS, Greenwood, B, Brandtzaeg, P. Epidemic meningitis, meningococcaemia, and neisseria meningitidis. Lancet 2007;369:2196–210. https://doi.org/10.1016/s0140-6736(07)61016-2.Suche in Google Scholar PubMed
4. Caugant, DA, PA Kristiansen, X Wang, LW Mayer, M-K Taha, R Ouédraogo, et al.. Molecular characterization of invasive meningococcal isolates from countries in the African meningitis belt before introduction of a serogroup a conjugate vaccine. United Kingdom: PLoS ONE; 2012, 7:e46019 p.10.1371/journal.pone.0046019Suche in Google Scholar PubMed PubMed Central
5. Campagne, G, Schuchat, A, Djibo, S, Ousseini, A, Cisse, L, Chippaux, J-P. Epidemiology of bacterial meningitis in Niamey, Niger, 1981-96. Bull World Health Organ 1999;77:499.Suche in Google Scholar
6. Irving, T, Blyuss, K, Colijn, C, Trotter, C. Modelling meningococcal meningitis in the African meningitis belt. Epidemiol Infect 2012;140:897–905. https://doi.org/10.1017/s0950268811001385.Suche in Google Scholar PubMed
7. Coen, P, Cartwright, K, Stuart, J. Mathematical modelling of infection and disease due to neisseria meningitidis and neisseria lactamica. Int J Epidemiol 2000;29:180–8. https://doi.org/10.1093/ije/29.1.180.Suche in Google Scholar PubMed
8. Vereen, K. An scir model of meningococcal meningitis. Virginia: Virginia Commonwealth University; 2008.Suche in Google Scholar
9. Karachaliou, A, Conlan, AJ, Preziosi, MP, Trotter, CL. Modelling long-term vaccination strategies with menafrivac in the African meningitis belt. Clin Infect Dis 2015;61:S594–600. https://doi.org/10.1093/cid/civ508.Suche in Google Scholar PubMed PubMed Central
10. Asamoah, JKK, Nyabadza, F, Seidu, B, Chand, M, Dutta, H. Mathematical modelling of bacterial meningitis transmission dynamics with control measures. Comput Math Methods Med 2018:21. https://doi.org/10.1155/2018/2657461.Suche in Google Scholar PubMed PubMed Central
11. Agier, L, Deroubaix, A, Martiny, N, Yaka, P, Djibo, A, Broutin, H. Seasonality of meningitis in Africa and climate forcing: aerosols stand out. J R Soc Interface 2013;10:20120814. https://doi.org/10.1098/rsif.2012.0814.Suche in Google Scholar PubMed PubMed Central
12. Yaga, SJ, Saporu, FWO. A study of a deterministic model for meningitis epidemic. J Epidemiol Methods 2024;13:20230023. https://doi.org/10.1515/em-2023-0023.Suche in Google Scholar
13. Bailey, NTJ. The mathematical theory of infectious diseases and its applications. London: Griffin; 1975.Suche in Google Scholar
14. Daley, DJ, J Gani. Epidemic modelling: an introduction. Cambridge: Cambridge University Press; 1999.Suche in Google Scholar
15. Stollenwerk, N, Maiden, MCJ, Jansen, VAA. Diversity of pathogenicity can cause outbreaks of meningococcal disease. Proc Natl Acad Sci USA 2004;101:10229–34. https://doi.org/10.1073/pnas.0400695101.Suche in Google Scholar PubMed PubMed Central
16. Sharew, A, J Bodilsen, BR Hansen, H Nielsen, CL Brandt. The cause of death in bacterial meningitis. BMC Infect Dis 2020;20:1–9. https://doi.org/10.1186/s12879-020-4899-x.Suche in Google Scholar PubMed PubMed Central
17. Bailey, NTJ. The elements of stochastic processes with applications to the natural sciences. New York: Wiley; 1964.Suche in Google Scholar
18. Isham, V. Stochastic models for epidemics with special reference to AIDS. Ann Appl Probab 1993;3:1–27. https://doi.org/10.1214/aoap/1177005505.Suche in Google Scholar
19. Keeling, MJ, Rohani, P. Modelling infectious diseases in humans and animals, 1st ed. Princeton, N.J.: Princeton University Press; 2008.10.1515/9781400841035Suche in Google Scholar
20. Lloyd, AL, Zhang, J, Root, A. Stochasticity and heterogeneity in host vector models. J R Soc Interface 2007;4:851–63. https://doi.org/10.1098/rsif.2007.1064.Suche in Google Scholar PubMed PubMed Central
21. Dietz, K, D Shenzle. Mathematical models for infectious disease statistics. New York, USA: Springer, A Celebration of Statistics; 1985:167–204 pp.10.1007/978-1-4613-8560-8_8Suche in Google Scholar
22. Whittle, P. The outcome of stochastic epidemic. A note on Baileys paper. Biometrika 1955;42:116–22. https://doi.org/10.2307/2333427.Suche in Google Scholar
23. Ludwig, D. Stochastic approximation for general epidemic. J Appl Probab 1973;10:263–76. https://doi.org/10.1017/s0021900200095279.Suche in Google Scholar
24. Gillespie, DT. Exact stochastic simulation of coupled chemical reactions. J Phys Chem 1977;81:2340–61. https://doi.org/10.1021/j100540a008.Suche in Google Scholar
25. Gillespie, DT. Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys 2001;115:1716–33. https://doi.org/10.1063/1.1378322.Suche in Google Scholar
26. Giesecke, J. Modern infectious disease epidemiology, 2nd ed. Florida, USA: Hodder Education; 2002.Suche in Google Scholar
27. Allen, LJS, Lahodny, GEJr. Extinction thresholds in deterministic and stochastic epidemic models. J Biol Dynam 2012;6:590–611. https://doi.org/10.1080/17513758.2012.665502.Suche in Google Scholar PubMed
28. Britton, T, House, T, Lloyd, AL, Mollison, D, Riley, S, Trapman, P. Five challenges for stochastic epidemic models involving global transmission. Epidemics 2015;10:54–7. https://doi.org/10.1016/j.epidem.2014.05.002.Suche in Google Scholar PubMed PubMed Central
29. Borrow, R, Caugant, DA, Ceyhan, M, Christensen, H, Dinleyici, EC, Findlow, J, et al.. Meningococcal disease in the middle east and Africa: findings and updates from the global meningococcal initiative. J Infect 2017;75:1–11. https://doi.org/10.1016/j.jinf.2017.04.007.Suche in Google Scholar PubMed
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Causal mediation analysis for difference-in-difference design and panel data
- Research Articles
- Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level
- Discrete-time compartmental models with partially observed data: a comparison among frequentist and Bayesian approaches for addressing likelihood intractability
- Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
- Investigating the association between school substance programs and student substance use: accounting for informative cluster size
- The quantiles of extreme differences matrix for evaluating discriminant validity
- Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions
- What if dependent causes of death were independent?
- Bot invasion: protecting the integrity of online surveys against spamming
- A study of a stochastic model and extinction phenomenon of meningitis epidemic
- Understanding the impact of media and latency in information response on the disease propagation: a mathematical model and analysis
- Time-varying reproductive number estimation for practical application in structured populations
- Perspective
- Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?
- Leveraging data from multiple sources in epidemiologic research: transportability, dynamic borrowing, external controls, and beyond
- Regression calibration for time-to-event outcomes: mitigating bias due to measurement error in real-world endpoints
Artikel in diesem Heft
- Causal mediation analysis for difference-in-difference design and panel data
- Research Articles
- Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level
- Discrete-time compartmental models with partially observed data: a comparison among frequentist and Bayesian approaches for addressing likelihood intractability
- Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
- Investigating the association between school substance programs and student substance use: accounting for informative cluster size
- The quantiles of extreme differences matrix for evaluating discriminant validity
- Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions
- What if dependent causes of death were independent?
- Bot invasion: protecting the integrity of online surveys against spamming
- A study of a stochastic model and extinction phenomenon of meningitis epidemic
- Understanding the impact of media and latency in information response on the disease propagation: a mathematical model and analysis
- Time-varying reproductive number estimation for practical application in structured populations
- Perspective
- Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?
- Leveraging data from multiple sources in epidemiologic research: transportability, dynamic borrowing, external controls, and beyond
- Regression calibration for time-to-event outcomes: mitigating bias due to measurement error in real-world endpoints
