Analysis of a model for waterborne diseases with Allee effect on bacteria
Articles
Florinda Capone
Universitá di Napoli Federico II
https://orcid.org/0000-0002-0672-999X
Maria Francesca Carfora
Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR
https://orcid.org/0000-0002-4570-1690
Roberta De Luca
Universitá di Napoli Federico II
https://orcid.org/0000-0002-2109-7564
Isabella Torcicollo
Istituto per le Applicazioni del Calcolo “Mauro Picone”, CNR
https://orcid.org/0000-0001-6374-4371
Published 2020-11-01
https://doi.org/10.15388/namc.2020.25.20563
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Keywords

waterborne disease
Allee effect
stability
ODEs system

How to Cite

Capone F., Carfora M. F., De Luca R. and Torcicollo I. (2020) “Analysis of a model for waterborne diseases with Allee effect on bacteria”, Nonlinear Analysis: Modelling and Control, 25(6), pp. 1035-1058. doi: 10.15388/namc.2020.25.20563.

Abstract

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown.

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