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Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive number<jats:italic>\u211b<\/jats:italic><jats:sub>0<\/jats:sub>plays a critical role as a threshold parameter. When analyzing a nontrivial equilibrium (e.g., an endemic, boundary, or coexistence equilibrium) where<jats:italic>\u211b<\/jats:italic><jats:sub>0<\/jats:sub>is explicit, we usually come across a typical result: if<jats:italic>\u211b<\/jats:italic><jats:sub>0<\/jats:sub>&gt;1, then a nontrivial equilibrium exists in the biological sense. However, for more sophisticated models,<jats:italic>\u211b<\/jats:italic><jats:sub>0<\/jats:sub>can be too complicated to be revealed in terms of the involving parameters; the task of relating the formulation of a nontrivial equilibrium to<jats:italic>\u211b<\/jats:italic><jats:sub>0<\/jats:sub>thus becomes intractable. This paper shows how to mitigate such a problem with the aid of functional analysis, adopting the framework of a nonlinear eigenvalue problem. An equilibrium equation is first to be transformed into a canonical equation in a lower dimension, and then the existence is confirmed under several conditions. Three models are tested showing the applicability of this approach.<\/jats:p>","DOI":"10.1515\/amcs-2017-0044","type":"journal-article","created":{"date-parts":[[2017,9,25]],"date-time":"2017-09-25T10:00:43Z","timestamp":1506333643000},"page":"623-636","source":"Crossref","is-referenced-by-count":8,"title":["On the existence of a nontrivial equilibrium in relation to the basic reproductive number"],"prefix":"10.61822","volume":"27","author":[{"given":"Karunia Putra","family":"Wijaya","sequence":"first","affiliation":[{"name":"Mathematical Institute , University of Koblenz , Universit\u00e4t Stra\u00dfe 1, 56070 Koblenz , Germany"}]},{"family":"Sutimin","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Diponegoro University , Jalan Prof. H. Soedarto, SH, 50275 Semarang , Indonesia"}]},{"given":"Edy","family":"Soewono","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Bandung Institute of Technology , Jalan Ganesha 10, 40132 Bandung , Indonesia"}]},{"given":"Thomas","family":"G\u00f6tz","sequence":"additional","affiliation":[{"name":"Mathematical Institute , University of Koblenz , Universit\u00e4t Stra\u00dfe 1, 56070 Koblenz , Germany"}]}],"member":"37438","published-online":{"date-parts":[[2017,9,23]]},"reference":[{"key":"2021040700393726904_j_amcs-2017-0044_ref_001_w2aab3b7c13b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Aguiar, M., Kooi, B.W., Rocha, F., Ghaffari, P. and Stollenwerk, N. (2013). 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