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Table 2 For different values of γ, we present the threshold (β 0 ) and lower bound ( β c q , for q = 0 and 1) of the transmission coefficients (all in years-1).

From: Assessing the effects of multiple infections and long latency in the dynamics of tuberculosis

  

p= 0.80

   

p= 0.01

   

γ

β 0

β c 0

β c 1

β 0 β c 0

β 0 β c 1

β c 0

β c 1

β 0 β c 0

β 0 β c 1

0.01

5.2676

--

4.7343

--

0.5333

--

--

--

--

0.001

34.442

5.1107

4.9438

29.3313

29.4982

--

--

--

--

0.0001

326.19

4.9763

4.9594

321.2137

321.2306

208.07

208.82

118.12

119.37

0.00001

3243.6

4.9626

4.9609

3238.6374

3238.6391

208.24

208.11

3035.4

3035.5

  1. In the last two columns we present the range over which backward bifurcation occurs ( β 0 β c q ). For γ = 0.001 years-1, we have no backward bifurcation for q = 0 ( β c 0 does not exist). We considered p = 0.8 and p = 0.01, and the values of other parameters are those given in Table 1.