Dynamics of herpes and chlamydia co-infection in a population

Figure 1.  Schematic diagram for the C. trachomatis-HSV co-infection model

Figure 2.  stability of $\mathcal{E}_{S}$ in the case where $\mathscr{R}_{C}<1$, and $\mathscr{R}_{H}<1$

Figure 3.  Existence of $\mathcal{E}_{CH}$ when $\mathscr{R}_{C}>1$, $\mathscr{R}_{H}>1$, and $\mathscr{R}_{CH}>1$

Figure 4.  Stability of $\mathcal{E}_{C}$ in the case where $\mathscr{R}_{C}>1$, and $\mathscr{R}_{H}<1$

Figure 5.  Stability of $\mathcal{E}_{H}$ in the case where $\mathscr{R}_{H}>1$, and $\mathscr{R}_{CH}<1$

Figure 6.  Figure illustrating existence of a co-infection equilibrium $ \mathcal{E}_{CH} $ when $ \mathscr{R}_{C} = 2.14861 $, $ \mathscr{R}_{H} = 1.9699, $ and $ \mathscr{R}_{CH} = 2.02736 $. The figure is a projection of the solution curves on the $ C-H $ plane and shows the convergence of solutions to the co-infection equilibrium starting from different initial points. Numerical values of the state variables at the equilibrium point are obtained to be $ S = 0.399268, C = 0.193693, H = 0.0339702, I_{HP} = 0.0833719, I_{LC} = 0.0471582 $, and $ L = 0.0786341 $. The numerical values of the eigenvalues are $ -0.262134 + 0.i, -0.162314 + 0.i, -0.0732374 + 0.00898703i, -0.0732374 - 0.00898703i, -0.0157534 + 0.0188849i, -0.0157534 - 0.0188849i $. Clearly, all eigenvalues have negative real parts

Figure 7.  Existence and stability diagram of equilibrium points depending on $ \mathscr{R}_{C} $, $ \mathscr{R}_{H} $ and $ \mathscr{R}_{CH} $. The global dynamics is fully described whenever $ \mathscr{R}_{CH}<1 $. Cross-marks denote combinations of reproduction numbers that are not possible