Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma

Figure 1.  The flow diagram of macrophages, T cells and bacteria

Figure 2.  The graph of functions $g_1$ and $g_2$ defined in (20).

Figure 3.  Standard regression coefficients (SCR) for $R_0 = \frac{\nu}{\gamma_U + \mu_{B}}$ assuming the values given in Table 1 for $\nu, \gamma_{U} = \bar \gamma\displaystyle{\Lambda_U \over \mu_U}$ and $\mu_{B}$

Figure 4.  Standard regression coefficients (SCR) for $R_1 = \frac{\bar r \bar\beta {\Lambda_U \over \mu}}{\gamma_U + \mu_{B}}$ assuming the values given in Table 1 for $\bar r, \bar \beta, \displaystyle{\Lambda_U \over \mu_U}, \gamma_{U} = \bar \gamma\displaystyle{\Lambda_U \over \mu_U}$ and $\mu_{B}$.

Figure 5.  The numerical simulations of temporal course for bacteria with ten initial conditions show the stability of the bacteria-present equilibrium $P_2$ and the infection free equilibrium $P_0$ given in (47) when $\sigma = 0.24$, $\sigma_c = 0.319$, $R_0 = 0.4$, $R_0 = 0.34$, $R_1 = 1.5$, $g_1(B^{\max}) = 1.37\times 10^{312}$ and $g_2(B^{\max}) = 1.32\times 10^{942}$.

Figure 6.  The numerical simulations of temporal course for bacteria with ten initial conditions show the stability of the bacteria-present equilibria $P_1$ a$P_3$ given in (48) when $\sigma = 2.4\times 10^{-6}$, $\sigma_c = 0.003$, $R_0 = 0.0045$, $R^*_0 = 0.0043$, $R_1 = 0.43$.

Figure 7.  The stable infection free equilibrium $P_0$ bifurcates to the stable bacteria-present equilibrium $P_1$ in the value $R_0 = 1-R_1$.

Figure 8.  The results suggest forward and backward bifurcations, and a type of S-shaped bifurcation