{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T18:23:34Z","timestamp":1770143014474,"version":"3.49.0"},"reference-count":42,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T00:00:00Z","timestamp":1549929600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2019,2,12]]},"abstract":"<jats:p>In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:math>. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>=<\/mml:mo><mml:mn mathvariant=\"normal\">1.1208<\/mml:mn><\/mml:math>. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mrow><mml:mi>\u03b2<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.<\/jats:p>","DOI":"10.1155\/2019\/8465747","type":"journal-article","created":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T18:33:04Z","timestamp":1549996384000},"page":"1-13","source":"Crossref","is-referenced-by-count":40,"title":["Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8260-8885","authenticated-orcid":true,"given":"Hailay Weldegiorgis","family":"Berhe","sequence":"first","affiliation":[{"name":"Pan African University Institute of Basic Sciences Technology and Innovation, Nairobi, Kenya"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4550-9591","authenticated-orcid":true,"given":"Oluwole Daniel","family":"Makinde","sequence":"additional","affiliation":[{"name":"Faculty of Military Science, Stellenbosch University, Cape Town, South 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