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Modelling and Analysis of Bacteria Dependent Infectious Diseases with Variable Contact Rates

J. B. Shukla1, Shikha Singh2, Jitendra Singh2, Sunil Kumar Sharma3,*

1 Innovative Internet University for Research, Kanpur, 208017, India
2 P.P.N.(P.G.) College, CSJM University, Kanpur, 208001, India
3 College of Computer and Information Sciences, Majmaah University, Majmaah, 11952, Saudi Arabia

* Corresponding Author: Sunil Kumar Sharma. Email:

Computers, Materials & Continua 2021, 68(2), 1859-1875.


In this research, we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases. It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives. In this model, we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat. The stability theory has been analyzed to analyzed to study the crucial role played by bacteria in the increased spread of an infectious disease. It is shown that as the density of non-emigrating population increases, the spread of an infectious disease increases. It is shown further that as the emigration increases, the spread of the disease decreases in both the cases of contact mentioned above rates, but this spread increases as these contact rates increase. It suggested that the control of bacteria in the human habitat is very useful to decrease the spread of an infectious disease. These results are confirmed by numerical simulation.


Cite This Article

J. B. Shukla, S. Singh, J. Singh and S. Kumar Sharma, "Modelling and analysis of bacteria dependent infectious diseases with variable contact rates," Computers, Materials & Continua, vol. 68, no.2, pp. 1859–1875, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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