Modelling Tuberculosis with Conditional Latent Period
- September 2, 2020
- Posted by: RSIS Team
- Categories: Clinical Sciences, IJRIAS
International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume V, Issue VI, June 2020 | ISSN 2454-6194
Modelling Tuberculosis with Conditional Latent Period
A. Z. Loko1*, Joseph I. K2, Alhaji Ismaila Sulaiman3, Lucas W. L.1
1Mathematics Department, Nasarawa State University, Keffi, P.M.B.1022, Keffi, Nigeria
2Physics Department, Nasarawa State University, Keffi, P.M.B.1022, Keffi, Nigeria
3Statistics Department, Nasarawa State University, Keffi, P.M.B.1022, Keffi, Nigeria
*Corresponding Author
Abstract:- In this research work, we modeled Tuberculosis (TB) with conditional latent period using Delay Differential Equation. The model variables were divided into six compartments – susceptible, vaccinated latent (low and high), infected and recovered humans. We investigate the Disease Free Equilibrium (DFE) of the model and find the conditions that guarantee the asymptotic stability of corresponding steady states using stability theory of differential equations. The numerical simulations were carried out to test the effect of influence of key parameters on the spread of the TB epidemic, in particular the treatment and vaccination parameters to support the analytical solution and the stability theorem. It was shown that the introduced vaccination, high latent period and treatment parameter helps in controlling and eradication of TB epidemic in the population with respect to time. It is good to conclude that high effective treatment should be administered as well as high vaccination as this helps a long way in controlling the TB epidemic.
Keywords: Tuberculosis, Conditional Latent Period, Vaccination, Local Stability, Disease Free Equilibrium
