ScholarLens Back to search
2018•World Journal of Research and ReviewOpen access

Local Stability of Equilibrium Points of a SIR Mathematical Model of Infectious Diseases

S. A. Egbetade, I. A. Salawu, P. A Rafiu Fasanmade

Open full text 4 citations

Abstract

In this paper, we studied a SIR mathematical model of infectious diseases. We formulate a theorem on existence and uniqueness of solutions and establish the proof of the theorem We showed that the model has two equilibrium points: disease-free and endemic equilibrium. Local stability of the equilibrium points was obtained using reliable Jacobian matrices and basic reproduction number (R0). The analysis reveals that the disease- free equilibrium is locally asymptotically stable if R0 lt1, the infection is temporalwill disappear with time. On the other hand, if nbspR0 gt1, the number of infections rises, an epidemic results and the nbspendemic equilibrium is locally stable.nbspnbsp

About this research paper

What this paper is about

In this paper, we studied a SIR mathematical model of infectious diseases. We formulate a theorem on existence and uniqueness of solutions and establish the proof of the theorem We showed that the model has two equilibrium points: disease-free and endemic equilibrium. Local stability of the equilibrium points was obtained using reliable Jacobian matrices and basic reproduction number (R0). The analysis reveals that the disease- free equilibrium is locally asymptotically stable if R0 lt1, the infection is temporalwill disappear with time. On the other hand, if nbspR0 gt1, the number of infections rises, an epidemic results and the nbspendemic equilibrium is locally stable.nbspnbsp

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper, we studied a SIR mathematical model of infectious diseases. We formulate a theorem on existence and uniqueness of solutions and establish the proof of the theorem We showed that the model has two equilibrium points: disease-free and endemic equilibrium. Local stability of the equilibrium points was obtained using reliable Jacobian matrices and basic reproduction number (R0). The analysis reveals that the disease- free equilibrium is locally asymptotically stable if R0 lt1, the infection is temporalwill disappear with time. On the other hand, if nbspR0 gt1, the number of infections rises, an epidemic results and the nbspendemic equilibrium is locally stable.nbspnbsp

Key concepts: Equilibrium point, Uniqueness, Basic reproduction number, Mathematics, Epidemic model, Applied mathematics, Mathematical economics, Jacobian matrix and determinant

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Local Stability of Equilibrium Points of a SIR Mathematical Model of Infectious Diseases — Research Paper | ScholarLens