Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment
Keywords:Model Penyebaran Penyakit Meningitis, Titik Kesetimbangan, Nilai Eigen
AbstractMeningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.
Agier, L., Martiny, N., Thiongane, O., Mueller, J. E., Paireau, J., Watkins, E. R., Broutin, H. (2017). Towards understanding the epidemiology of Neisseria meningitidis in the African meningitis belt: a multi-disciplinary overview. International Journal of Infectious Diseases, 54, 103-112. doi:10.1016/j.ijid.2016.10.032
Asamoah, J. K. K., Nyabadza, F., Seidu, B., Chand, M., & Dutta, H. (2018). Mathematical modelling of bacterial meningitis transmission dynamics with control measures. Computational and Mathematical Methods in Medicine, 1-21. doi:10.1155/2018/2657461
Blyuss, K. B., (2016). Mathematical modelling of the dynamics of meningococcal meningitis in Afrika. UK Success Stories in Industrial Mathematics, 221-226. doi:10.1007/978-3-319-25454-8_28
Brauer, F. & Castillo-Chavez, C., (2012). Mathematical Models in Population Biology and Epidemiology. Second Edition. New York: Springer.
Broutin, H., Philippon, S., Constantin de Magny, G., Courel, M.-F., Sultan, B., & Guégan, J.-F. (2007). Comparative study of meningitis dynamics across nine African countries: a global perspective. International Journal of Health Geographics, 6(1), 29. doi:10.1186/1476-072x-6-29
Martcheva, M., & Crispino-O'Connell, G. (2003). The Transmission of meningococcal infection: a mathematical study. Journal of Mathematical Analysis and Applications, 283(1), 251-275. doi:10.1016/s0022-247x(03)00289-0
Martínez, M. J. F., Merino, E.G., Sánchez, E.G., Sánchez, J. E. G., Rey, A. M. del, & Sánchez, G. R. (2013). A mathematical model to study the meningococcal meningitis. International Conference on Computational Science, 18, 2492-2495. doi:10.1016/j.procs.2013.05.426
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