Time Scale Separation in the Vector Borne Disease Model SIRUV via Center Manifold Analysis

We investigate time scale separation in the vector borne disease model SIRUV, as previously described in the literature [1], and recently reanalyzed with the singular perturbation technique [2]. We focus on the analysis with a single small parameter, the birth and death rate µ, whereas all other model parameters are much larger and describe fast transitions. The scaling of the endemic stationary state, the Jacobian matrix around it and its eigenvalues with this small parameter µ is calculated and the center manifold analysis performed with the method described in [3] which goes back to earlier work [4, 5], namely a transformation of the Jacobian matrix to block structure in zeroth order in the parameter µ is used and then a family of center manifolds with µ larger than zero is obtained.