A mathematical model for the impact of disinfectants on the control of bacterial diseases

Abstract

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

Keywords:

• Epidemic model
• awareness
• disinfectants
• stability
• sensitivity

Acknowledgments

All the authors express their gratitude to the associate editor and the reviewers whose comments and suggestions have helped in improving this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Rabindra Kumar Gupta is thankful to UGC Nepal for partial financial support in the form of ‘PhD Fellowship and Research Support’ (No. PhD/76-77 S&T-17).