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Computational Ecology and Software, 2020, 10(2): 59-73
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Article

Role of environmental factors on the spread of bacterial diseases: A modeling study

Sandhya Rani Verma1, Ram Naresh1, Manju Agarwal2, Shyam Sundar3
1Department of Mathematics, School of Basic and Applied Sciences, Harcourt Butler Technical University, Kanpur-208002, India
2Department of Mathematics and Astronomy, University of Lucknow, Lucknow-226007, India
3Department of Mathematics, P. S. Institute of Technology, Kanpur-208020, India

Received 18 January 2020;Accepted 22 February 2020;Published 1 June 2020
IAEES

Abstract
In this paper, a nonlinear mathematical model is proposed and analyzed to study the role of cumulative environmental degradation on the spread of bacterial diseases. In the modeling process, it is assumed that the disease is not only transmitted directly from the infective population to susceptible population but also indirectly by the bacteria present in the conducive degraded environment. The cumulative density of the bacteria population is assumed to be governed by a generalized logistic model, and is also dependent on conducive environmental degradation. The cumulative density of environmental degradation is assumed to be dependent on human population-related factors. The analysis of the model is performed by using the stability theory of differential equations and numerical simulation. The model analysis reveals that the increased rate of conducive environmental degradation increases the density of bacteria population which leads to fast spread of the bacterial diseases.

Keywords mathematical modeling;stability;bacterial diseases;environmental degradation;simulation.


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