Dynamics of a waterborne pathogen model under the influence of environmental pollution

Sandeep Sharma and Nitu Kumari

Applied Mathematics and Computation, 2019, vol. 346, issue C, 219-243

Abstract: A non-linear mathematical model is proposed and analyzed to capture the role of environmental pollution on the spread of waterborne diseases. We calculate the threshold quantity (i.e. the basic reproduction number) for the proposed model. It is observed that model possesses two equilibria, namely disease free equilibrium and endemic equilibrium. The disease free equilibrium is globally asymptotically stable when the basic reproduction number is less than or equal to one. If the basic reproduction number exceeds one then the disease persists and endemic equilibrium point is globally asymptotically stable under certain conditions. The conditions of global stability of the endemic equilibrium are obtained using the compound matrix. The dynamical study of our model provides a clear insight of the role of pollution on the spread of waterborne diseases. An increase in the size of infected population with increase in the stress related parameters demonstrates that environmental pollution increases the size of the epidemics. Despite the severity of the issue, little efforts have been made in this direction. We firmly believe that our study will bridge this gap and help the authorities forming policies to combat fatal waterborne diseases.

Keywords: Waterborne diseases; Environmental pollution; Persistence; Backward bifurcation; Stability (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630031830910X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:219-243

DOI: 10.1016/j.amc.2018.10.044

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().