Math. J. Interdiscip. Sci.

Mathematical Model for Impact of Media on Cleanliness Drive in India

N H Shah, J S Patel, F A Thakkar and M H Satia

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Mathematical model; Active cleaners; Passive cleaners; Media; Simulation

PUBLISHED DATE September, 2018
PUBLISHER The Author(s) 2018. This article is published with open access at

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.


Maintaining a clean environment plays an important role in the health of every human being, because their health is fully based on the surrounding environment. The importance of cleanliness cannot be ignored by any society. Every religion and civilization emphasis the significance of cleanliness. It is a virtue of God. Woefully, this virtue of cleanliness not reflected in our society. People usually throw garbage in the roads, streets and gardens etc. Spitting anywhere is also common practice. Students of schools and colleges also throw waste in the classroom and the other premises. pitiful conditions about cleanliness are observed in our society. We must develop positive attitude to tackle this situation. In fact, there is a need to inspire people about importance of cleanliness in our life [4].

Taking in to the account the urgent need of cleanliness in India, the Prime Minister Narendra Modi had launched cleanliness drive as “Swachh Bharat Abhiyan” on 2nd October 2014, at Rajghat, New Delhi [3]. The objectives of the cleanliness drive in India are to clean up houses, streets, roads and infrastructure of India’s cities, smaller towns, and as well as eliminating open defecation in rural areas [4]. The cleanliness drive aims to achieve the vision of ‘Clean India’ by 2nd October 2019. Each citizen of India should join in this cleanliness drive as ‘cleaner’ to achieve the goal of “Swachh Bharat Abhiyan”.

There are two types of cleaners, namely ‘active cleaners’ and ‘passive cleaners’. Active cleaners are involved in cleanliness activity with their own interest, while passive cleaners need an external force to engage in cleanliness related activity. It is observed that media plays vital role as motive force for passive cleaners to join in cleanliness drive and become active media happens to be the most readily available and potentially most economical means of spreading information about cleanliness drive. Media can effectively lift public awareness and concern about sanitation. Moreover, every day public see a lot of advertisements in electronic and print media, where they tell people to support this drive (Pradhan, 2017). Eventually, the media works as stimulant in cleanliness drive. (Shah et al. 2018) developed a mathematical model for cleanliness drive and has discussed its stability through graph theory.

In this paper, we will analyse how passive cleaners turns to be active cleaners under impact of media. In section 2, a mathematical model is discussed with schematic diagram along with notations, description and parametric values as described in Table 1. Local and global stability of the equilibrium points are discussed in section 3.1 and 3.2 respectively. Section 4 studies optimal control on the system. In section 5, numerical simulation of the model is carried out and interpretations are work out.

Page(s) 29-36
ISSN Print: 2278-9561, Online: 2278-957X

In this paper, a mathematical model of cleanliness drive in India is studied. One can conclude that media is essential for the awareness of cleanliness among individuals since passive cleaners become active cleaners in cleanliness related activities comparatively at a higher rate when media impact is observed. Our first contribution for the clean India is to keep our house clean by proper wastage management of our house as per the instruction of the corporation. We should also actively participate in the cleanliness drive to clean our streets, school, college, office, public place etc. to achieve vision of ‘Clean India’. This model can be extended to various social and health related issues. Infectious diseases usually spread in unhygienic environment. Cleanliness play vital role to control it. Hence, the model can be extended to study the effect of cleanliness in controlling infectious diseases.

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