Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

Abstract

Meningitis 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.

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“…Contohnya adalah penyebaran penyakit TBC, Demam Berdarah (DBD) atau HIV-AIDS dan lainlain. [3][4][5][6][7][12][13]. Model matematika mengenai penyebaran COVID-19 juga telah banyak diteliti oleh banyak peneliti yang mengkaji tentang dinamika penyebaran penyakit tersebut dalam populasi [2,[8][9][10][11]14].…”

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“…Kontrol optimal dengan menggunakan vaksinasi dan pengobatan pada model SEIR menunjukkan bahwa dengan memberikan vaksinasi pada populasi rentan dan pengobatan pada populasi terinfeksi dapat mengontrol penyebaran virus Covid-19 [8]. Model matematika mengenai dinamika penyebaran dalam populasi Covid-19 juga telah banyak dikaji oleh peneliti [9][10][11][12][13].…”