{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T06:30:46Z","timestamp":1781332246666,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,10,27]],"date-time":"2020-10-27T00:00:00Z","timestamp":1603756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra\u2013Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra\u2013Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra\u2013Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.<\/jats:p>","DOI":"10.3390\/sym12111778","type":"journal-article","created":{"date-parts":[[2020,10,29]],"date-time":"2020-10-29T23:06:12Z","timestamp":1604012772000},"page":"1778","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["An Approach for the Global Stability of Mathematical Model of an Infectious Disease"],"prefix":"10.3390","volume":"12","author":[{"given":"Mojtaba","family":"Masoumnezhad","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Chamran, Guilan Branch, Technical and Vocational University (TVU), Tehran 1435761137, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4747-0945","authenticated-orcid":false,"given":"Maziar","family":"Rajabi","sequence":"additional","affiliation":[{"name":"Department of Software Engineering, University of Applied Science and Technology, Shabestar, Tabriz 5164864763, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2258-3449","authenticated-orcid":false,"given":"Amirahmad","family":"Chapnevis","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran 1591634311, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0815-4472","authenticated-orcid":false,"given":"Aleksei","family":"Dorofeev","sequence":"additional","affiliation":[{"name":"Head of Department of Propaedeutics of Dental Diseases, I.M. Sechenov First Moscow State Medical University, 119991 Moscow, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5829-8634","authenticated-orcid":false,"given":"Stanford","family":"Shateyi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Narges Shayegh","family":"Kargar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Payame Noor University (PNU), Tehran 193953697, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2521-1325","authenticated-orcid":false,"given":"Hassan Saberi","family":"Nik","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Neyshabur, Neyshabur 9319774446, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Anderson, R.M., and May, R.M. 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