Stability and Bifurcation Analysis of Mathematical Models of Meningitis Transmission with Vaccination and treatment

Rabiatul Adawiyah; Syamsuddin  Toaha; Kasbawati Kasbawati

doi:10.20956/j.v18i3.19714

Authors

Rabiatul Adawiyah Universitas Hasanuddin
Syamsuddin Toaha
Kasbawati Kasbawati

DOI:

https://doi.org/10.20956/j.v18i3.19714

Keywords:

Model of Meningitis Disease, Sensitivity of R_0, Bifurcations

Abstract

Meningitis is an infectious disease that occurs in inflammation of the meninges and the spinal cord in consequence of bacteria and viruses. Vaccination and treatment using antibiotics is used to increase growth rate in infected people so that the spread rate can be reduced. This study aims to see the effect of vaccination and treatment using some compartments: susceptible, carrier, infected without symptoms, infected with symptoms, recovery without disability, and recovery with disability; show the sensitivity analysis in order to discover the parameter that affect basic reproduction number and bifurcations analysis. The result from sensitivity found the relation between parameter and that can increase and decrease the value. This study also showed the influence of stability change from equilibrium point caused by the parameter value change form bifurcations analysis. Models simulation show that the effect of vaccination and treatmen for spread of meningitis can be handled.

References

Afifah, I., 2019. Analisis Kestabilan Global Model Penyebaran Penyakit Meningitis dengan Menggunakan Fungsi Lyapunov. Buletin Ilmiah Math, Stat, dan Terapannya, Vol. 8, No. 4, 829-838.

Afolabi, M.A., Adewoye, K.S., Folorunso, A.I., Omoloye, M.A., 2021. A Mathematical Model on Transmission Dynamic of Meningococcal Meningitis. IRE Journal, Vol 4, No. 10.

Alemneh, H.T. & Alemu, N.Y., 2021. Mathematical Modelling with Optimal Control Analysis of Social Media Addiction. KeAi Publishing, Vol 6, No. 21, 405-419.

Asamoah, J.K.K., Nyabadza, F., Jin, Z., Bonyah, E., Khan, M.A., Li, M.Y., & Hayat, T., 2020. Backward bifurcation and Sensitivity Analysis for Bacterial Meningitis Transmission Dynamic with A Nonlinear Recovery Rate. Chaos, Solitons, and Fractals, Vol 140.

Asamoah, J.K.K., Nyabadza,F., Seidu, B., Chand, M., & Duta, H., 2018. Mathematical Modelling of Bacterial Meningitis Transmission Dynamic with Control Measures. Computation and Mathematical Methods in Medicine, 1-21.

Brauwer, M., Tunkel, A. & Van de Beek, D., 2010. Epidemology, Diagnosis, and Antimicrobial Treatment of Acute Bacterial Meningitis. Clinical Microbiology, Vol 23, N. 3, 467-492.

Fajri, N., Sianturi, P., & Bakhtiar, T., 2015. Model Matematika SIS-SI dalam Penyebaran Penyakit Malaria dengan Vaksinasi Taksempurna. Institut Pertanian Bogor.

Gumel, A.B., 2012. Cause of Backward Bifurcations in some Epidemological Models. Journal of Mathematical Analysis and Applications, Vol. 395, No. 12, 355-365

Ibrahim, M.E. & Salma, O.A.A., 2017. A Mathematical Model for Meningitis Disease. Red Sea University Journal, Vol 2, No. 2, 467-472.

IDAI., 2015. Melengkapi/mengejari Imunisasi (Bagian III). https://www.idai.or.id/artikel/klinik/imunisasi/melengkapi-mengejar-imunisasi-bagian-iii [3 Juni 2021].

Kementrian Kesehatan., 2013. Selamatkan Jemaah Haji dan Umroh dari Bahaya Meningitis Meningokokus. https://www.kemkes.go.id/article/view/2277/selamatkan-jemaah-haji-dan-umroh-dari-bahaya-meningitis-meningokokus.html [1 Juni 2021].

Kementrian Kesehatan., 2019. Panduan Deteksi dan Respon Penyakit Meningitis Meningokokus. https://infeksiemerging.kemkes.go.id/PANDUAN_DETEKSI_RESPON_MM [28 Desember 2021]

Maimati, N., Isa, M.Z., Rahimi, A., Kouadio, I.K.,Ghazi, H.F. & Aljunid, S.M., 2012. Incidence of Bacterial Meningitis in South East Asia Region. BMC Public Health, Vol. 12, No. A30.

Martinez, M.J.F., Merino, E.G., Sanchez, E.G., Sanchez, J.E.G., Rey, A.M.D., & Sanchez G.R., 2013. A Mathematical Model to Study the Menigococcal Meningitis. Procedia Computer Science, Vol 18, 2492-2495.

Musa, S.S., Zhao, S., Hussaini, N., Habib, A.G., & He, D., 2019. Mathematical Modeling and Analsis of Meningococcal Meningitis Transmission Dynamic. International Journal of Biomathematics 2050006.

Side, S. & Rangkuti, Y.M., 2015. Pemodelan Matematika dan Solusi Numerik untuk Penularan Demam Berdarah. Perdana Publising.

WHO., 2018. Meningitis Meningococcal. https://www.who.int/emergencies/diseases/meningitis/epidemiological/en/ [9 April 2021]

Wiah, E.N. & Adetunde, I.A., 2010. A Mathematical Model of Cerebrospinal Meningitis Epidemic: A Case Study for Jirapa District, Ghana. KMITL Sci Tech J, Vol 10, No. 2.