A Theoretical Assessment of the Effects of Smoking on the Transmission Dynamics of Tuberculosis

Abstract

Smoking has long being associated with tuberculosis. We present a tuberculosis dynamics model taking into account the fact that some people in the population are smoking in order to assess the effects of smoking on tuberculosis transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Qualitative analysis of the model including positivity and persistence of solutions are presented. The model is numerically analyzed to assess the effects of smoking on the transmission dynamics of tuberculosis. Numerical simulations of the model show that smoking enhances tuberculosis transmission, progression to active disease and in a population of smokers, tuberculosis cannot be controlled even when treatment success is assumed to be as high as 88%. Further, analysis of the reproduction numbers indicates that the number of active tuberculosis cases increases as the number of smokers increase.

Optimal intervention strategy for prevention tuberculosis using a smoking-tuberculosis model

“…Some smoking-TB parameters are obtained from previous studies [9,7,18]. Once the other parameters have been determined, the parameters related to TB incidence α, k, and σ are fitted to TB incidence and TB relapse data using a least-squares fitting method.…”

Transmission dynamics of Trichomonas vaginalis and HIV/AIDS coinfection

“…In Table 11, a* denotes parameter values and ranges from Bhunu et al [3], b* denotes parameter values from Catterall [7], c* denotes parameter values from Weston and Nicol [29], d* denotes parameter values from Bhunu et al [4], e* denotes parameter values from Mukandavire and Garira [20], f* denotes parameter values from Gulmezoglu and Garner [11], g* denotes parameter values from Mavedzenge et al [17], h* denotes parameter values from Van Der Pol et al [27], i* denotes parameter values from NationMaster and j* denotes assumed parameter values. Fig.…”

Transmission dynamics of Trichomonas vaginalis: A mathematical approach

“…In the United States, it was recently estimated that 5 million new cases appear annually [27,33,7,10] compared with 3 million cases of chlamydia and 650 000 cases of gonorrhea annually. The epidemiology of the disease is still poorly understood and some practitioners continue to question its importance [3]. Trichomanas vaginalis is more prevalent in females (67%-100% female sexual partners of infected man get infected) than in males (14%-60% of male sexual partners of an infected woman get infected) [1,16,13].…”

“…Malaria, Tuberculosis, Hepatitis B, HIV/AIDS and other sexually transmitted infections have all being mathematically accounted for (see [28,2,24,31,22,25] to mention just a few of them). Quite recently some authors [34,19] did analyse some general SIR and SEIRS models with interesting dynamics.…”