Stability analysis of an enteropathogen population growing within a heterogeneous group of animals

Figure Scheme 1.   

Figure 1.  Bifurcation diagram showing epidemic progression (dark regions) or eradication (white regions) in a system with two hosts. The changing parameters are the fraction of bacteriophage given to the first host ($q_0^1/(q_0^1+q_0^2)$ ranging from 0 to 1) and its detachment rate ($\delta_1$ ranging from 0 to 1.5). The bacterial and bacteriophage distributions along the intestine once the system has converged to the equilibria are shown for two different set of parameters A and B. The dashed line refers to attached bacteria while gray color is used for host one and black for host two. The other fix parameters used to do the numeric simulations are the total bacteriophage dose per time unit $q_0^1+q_0^2=11$ and: $c_h=l_h=1$, $\gamma_1^h(u)=1-u$, $\gamma_2^h(v)=1-v$, $\alpha_h =4$, $b=4$, $\kappa_1^h=0.06$, $\kappa_2^h=0.1$, $\lambda_1^h=\lambda_2^h=0.1$, $\mu_1=0.4$ and $\mu_2=0.1$ for all $h\in{1,2}$ and $\delta_2=0.5$. Notice that the two hosts only differ in their detachment rate ($\delta_1$ and $\delta_2$) and the treatment received ($q_0^1$ and $q_0^2$).