Open AccessStability Analysis of an SIR Infectious Disease Model
Author(s) -
Dorcas Ezekiel,
S.A . Iyase,
T. A. Anake
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2199/1/012035
Subject(s) - hopf bifurcation , matlab , stability (learning theory) , bifurcation , epidemic model , qualitative analysis , mathematics , control theory (sociology) , steady state (chemistry) , computer science , medicine , physics , population , nonlinear system , qualitative research , artificial intelligence , social science , chemistry , control (management) , environmental health , quantum mechanics , machine learning , sociology , operating system
The paper investigates the stability of the SIR mathematical model of transmission of an infectious disease with delay. First, the study investigates local stability of the positive steady state of an infectious disease model by analyzing the linearised system where more general stability criteria with delay and model parameters are obtained. Secondly, the study shows that the model exhibits Hopf bifurcation on choosing the delay as a bifurcation parameter. Conditions for existence of qualitative behaviour for positive steady state are identified. Finally, numerical simulation of results and biological interpretations were verified using MATLAB software for the delay model. The study supplements theoretical improvement to earlier results obtained in the literature.