A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea

What Does a Mathematical Model Tell About the Impact of Reinfection in Korean Tuberculosis Infection?

“…As studied in the earlier work, the standard SEIL compartmental model is taken as the base model for the TB transmission dynamics, which uses the Korean demographic parameters [13]. In addition, the exogeneous reinfection has been incorporated in the model (the mathematical model is given below).The new TB transmission model classifies individuals as the susceptible class ( S ), the exposed class( E ), (or high-risk latent, that is, recently exposed but not yet infectious), the active-TB infectious class ( I ), and the low risk latent class or treated infected class ( L ).$\begin{array}{l}left\frac{dS}{dt}=\text{Λ}-\beta cS\frac{I}{N}-\mu S\hfill \\ left\frac{dE}{dt}=\beta cS\frac{I}{N}-p\beta cE\frac{I}{N}-\left(\mu +k+\alpha \right)E+\sigma \beta cL\frac{I}{N}\hfill \\ left\frac{dI}{dt}=p\beta cE\frac{I}{N}+kE-\left(\mu +\gamma +d\right)I\hfill \\ left\frac{dL}{dt}=\gamma I-\sigma \beta cL\frac{I}{N}-\mu L+\alpha E\hfill \\ leftN=S+E+I+L\hfill \end{array}$…”

“…In particular, the situation of the Republic of Korea such as a high latent ratio, exogenous reinfection should be a part of the model and it might play a key role in the Korean TB transmission. Recently, a Korean TB dynamical model has been developed including time-dependent coefficients and further optimal control theory has been employed to observe what would be more effective control measures to minimize the number of infected and exposed individuals [13]. In this manuscript, we modify this existing model by incorporating the exogeneous reinfection term from the work [12].…”

Optimal control in epidemiology

“…Since economic resources are limited, epidemiological models have started taking into consideration the economic constraints imposed by limited resources when analyzing control strategies. Optimal control theory has been applied to the mathematical models of HIV models Zarei et al (2010), Kwon et al (2012), Karrakchou et al (2006), Kwon (2007), Roshanfekr et al (2014), , Zhou et al (2014), Adams et al (2005), Costanza et al (2013), Orellana (2011), Malaria Okosun et al (2013, Okosun et al (2011), Okosun and Makinde (2014), Okosun (2011), Kim (2012), Prosper et al (2014), Tuberculosis Moualeu et al (2015), Silva and Torres (2013), Agusto and Adekunle (2014), Bowong and Aziz Alaoui (2013), Whang et al (2011), Vector borne diseases Lashari (2012), Graesboll et al (2014), Sung Lee and Ali Lashari (2014) and other diseases Yan and Zou (2008), Agusto (2013), Brown andJane White (2011), Zaman et al (2008), Okosun and Makinde (2014), Su and Sun (2015), Buonomo et al (2014), Lowden et al (2014), Roshanfekr et al (2014), Apreutesei et al (2014), Imran et al (2014).…”

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

“…The results demonstrate the confidence in the parameter estimates. [11], [49] μ natural death rate 0.0126 yr −1 [11], [49] TB …”