A Mathematical Study of a TB Model with Treatment Interruptions and Two Latent Periods

Table 1

Model parameters and their interpretations.

Definition	Symbol	Estimate
Recruitment rate	Λ	10,000/1.7
Natural death rate	𝜇	1/70
TB induced death rate in class 𝐼	𝑑1	0.5
TB induced death rate in class 𝑇	𝑑2	0.1
TB induced death rate in class 𝐷	𝑑3	0.2
Transmission coefficient from class 𝐼 to 𝑆	𝛽1	5𝛽2
Transmission coefficient from class 𝑇 to 𝑆	𝛽2	Variable
Transmission coefficient from class 𝐷 to 𝑆	𝛽3	1.5𝛽2
Reactivation rate of the early latent persons	𝑘	0.08
Reactivation rate of the later long-term latent persons	𝜔	0.2
Self-cured rate of the persons in class 𝐷	𝜂	0.02
Treatment rate of untreated active TB cases in class 𝐼	𝑟	0.3
Recovery rate of the treated active TB cases	𝜉	0.1
Rate of treatment interruptions	𝛾	0.1
Fraction of the early latent persons who progress TB fast	𝑝	0.075
Fraction of the self-cured persons in class 𝐷 who enter class 𝐸2	𝑞	0.9