Modeling the Spread of Tuberculosis in Semiclosed Communities

Table 3

Qualitative behaviour for system (1) as function of the disease transmission rate 𝛽, when the condition 𝛽_𝐵<𝛽_𝐶<𝛽_𝑅0 is fulfilled. Here, Δ₁ is the discriminant of the cubic polynomial (20).

Interval	Coefficients	Type of equilibrium
𝛽<𝛽𝐵	𝐴>0, 𝐵>0, 𝐶>0, 𝐷>0	Disease-free equilibrium
𝛽𝐵<𝛽<𝛽𝐶	𝐴>0, 𝐵<0, 𝐶>0, 𝐷>0	Two equilibria (Δ1<0) or none (Δ1>0)
𝛽𝐶<𝛽<𝛽𝑅0	𝐴>0, 𝐵<0, 𝐶<0, 𝐷>0	Two equilibria (Δ1<0) or none (Δ1>0)
𝛽𝑅0<𝛽	𝐴>0, 𝐵<0, 𝐶<0, 𝐷<0	Unique endemic equilibrium