Dynamics of amoebiasis transmission: stability and sensitivity analysis
type: Item
instance of: scholarly article
title: Dynamics of amoebiasis transmission: stability and sensitivity analysis
zbMATH Open document ID: 1394.92123
author: Fidele Hategekimana
author: Snehanshu Saha
author: Anita Chaturvedi
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: Compartmental epidemic models are intriguing in the sense that the generic model may explain different kinds of infectious diseases with minor modifications. However, there may exist some ailments that may not fit the generic capsule. Amoebiasis is one such example where transmission through the population demands a more detailed and sophisticated approach, both mathematical and numerical. The manuscript engages in a deep analytical study of the compartmental epidemic model; susceptible-exposed-infectious-carrier-recovered-susceptible (SEICRS), formulated for Amoebiasis. We have shown that the model allows the single disease-free equilibrium (DFE) state if \(R_0\), the basic reproduction number, is less than unity and the unique endemic equilibrium (EE) state if \(R_0\) is greater than unity. Furthermore, the basic reproduction number depends uniquely on the input parameters and constitutes a key threshold indicator to portray the general trends of the dynamics of Amoebiasis transmission. We have also shown that \(R_0\) is highly sensitive to the changes in values of the direct transmission rate in contrast to the change in values of the rate of transfer from latent infection to the infectious state. Using the Routh-Hurwitz criterion and Lyapunov direct method, we have proven the conditions for the disease-free equilibrium and the endemic equilibrium states to be locally and globally asymptotically stable. In other words, the conditions for Amoebiasis ``die-out'' and ``infection propagation'' are presented.
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6898687
zbMATH Keywords: amoebiasis
zbMATH Keywords: entamoeba histolytica
zbMATH Keywords: transmission model
zbMATH Keywords: basic reproduction number
MaRDI profile type: Publication
full work available at URL: math5040058
OpenAlex ID: W2766084607
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DOI: 10.3390/MATH5040058
description: scientific article; zbMATH DE number 6898687