Spread of Tuberculosis Among Smokers: A Mathematical Model

Spread of Tuberculosis Among Smokers: A Mathematical Model

Purvi M. Pandya (Department of Mathematics, Gujarat University, Ahmedabad, India), Ekta N. Jayswal (Department of Mathematics, Gujarat University, Ahmedabad, India) and Yash Shah (GCS Medical College, Ahmedabad, India)
Copyright: © 2020 |Pages: 25
DOI: 10.4018/978-1-7998-3741-1.ch003

Abstract

Smoking tobacco has some hazardous implications on an individual's physical, physiological, and psychological health; health of the passive smokers near him or her; and on the surrounding environment. From carcinomas to auto-immune disorders, smoking has a role to play. Therefore, there arises a need to frame a systemic pathway to decipher relationship between smoking and a perilous disease such as tuberculosis. This research work focuses on how drugs or medications can affect individuals who are susceptible to tuberculosis because of smoking habits and also on individuals who have already developed symptoms of tuberculosis due to their smoking addiction. The mathematical model is formulated using non-linear ordinary differential equations, and then threshold is calculated for different equilibrium points using next generation matrix method. Stability analysis along with numerical simulations are carried out to validate the data.
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Introduction

One of the most crucial yet common issue that humans can face, are health issues. It may be attributed to earning their livelihood. It sometimes shudders mental health of people who can’t withstand them positively. These causes mental imbalance which sometimes leads to behavioral changes and also becomes the reason for life-threatening habits such as smoking, drinking, drugs addiction etc. Smoking which is found to be very common among all age groups may lead to pulmonary, hepatic, cardiac or gastrointestinal diseases, carcinomas, ulcers, etc. turning out to be the main reasons for extensive mortality and morbidity all around the world. People adopt these habits for the sake of pleasure or as a form of stress release or succumbing to peer pressure. Disease like tuberculosis has become common issue among smokers. It can be cured if they complete prescribed course within a given time interval. Also, advanced medical science has helped to curtail severity of health issues prevailing among smokers by utilizing novel methods such as nicotine containing chewing gum, nicotine patch, nicotine spray, nicotine based nasal formulations etc. Different advanced programs are also developed in various areas to spread awareness regarding how to use new methods affectively to quit smoking.

Many researchers have given extraordinary contributions to this field opening new insights of customized and impactful drug delivery system. Several theoretical as well as practical aspects were brought into light. An epidemiological relation between smoking and individuals suffering from tuberculosis was reviewed from the UK, India, china and the USA (Davies et al., 2006). Also, a question was discussed to whether the age of individual matters on the impact of cigarette smoking on tuberculosis (Feng et al., 2014). Even many statistical analyses were done along with surveys of different areas. To visualize the transmission dynamics and spread of the disease many deterministic models are designed. The basic models such as SIS, SIR, SIRS, SEIR, SEIRS, etc. were constructed to study the transmission of tuberculosis among smokers along with many latent stages using different conditions and assumptions. A compartmental mathematical model to estimate the impact of tuberculosis and its control was projected together with incorporated changing trends in smoking (Basu et al., 2011). Models are constructed with different latent stages for tuberculosis transmission found in the regions of Asia-pacific (Trauer et al., 2014). Also, modelling and data analysis for tuberculosis epidemic in Russia (Perelman et al., 2004), model of tuberculosis with drug resistance effect (Ronoh et al., 2016), model to simulate disease among population with stability analysis (Koriko and Yusuf, 2008), global dynamics of tuberculosis containing three stages susceptible, latent and active stage (Guo, 2005) and global stability with early latent stage (Guo and Li, 2006) were discussed. A model with exogenous reinfection for tuberculosis consisting of four compartments (Feng et al., 2000), model with recurrent infection and vaccination based on SEIR-model with force of infection for tuberculosis (Nainggolan et al., 2013), practical aspects of backward bifurcation with seven compartments containing both fast and slow progression levels of infection and two different models (Gerberry, 2016), model concluding the prospects of controlling and improving case detection of tuberculosis (Okuonghae and Omosigho, 2011) were formulated and analyzed. So, different models along with stability analysis, bifurcation analysis, etc. were explored and analyzed. An epidemiological model with six compartments containing uninfected, latent stage and highly infected stage was considered as well. This was to investigate the effects of different cases on tuberculosis (murphy et al., 2002). Later an extension to this model was formulated and the influence of backward bifurcation was modelled to study the transmission of epidemic tuberculosis with reinfection (Singer and Kirschner, 2004). Even many case-control studies were conducted related to smoking and death in India (Jha et al., 2008). A similar eco-epidemiological model was formulated for prey and predators with saturated incidences (Saifuddin et al., 2016), the stability analysis, existence of equilibrium points, etc. of this model was also discussed (Saifuddin et al., 2017) and the epidemiological association between Smoking and tuberculosis and immunopathogenesis was discussed (Davies et al., 2006). A study on tuberculosis recurrences was done and concluded that it plays a very important role in certain population and they can again be infected easily (De Viedma et al., 2002).

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