Singular manifolds and bifurcations for a class of epidemic models

The existence and stability of singular manifolds for a class of minimum epidemic models based on family testing and tracing are studied by qualitative theory of differential equations. The necessary and sufficient conditions for the existence and stability of singular manifolds are presented and the non-parametric trans-critical bifurcations near singular manifolds are investigated. Finally, numerical simulations are conducted to verify the stability of the model by aid of Matlab software under the condition of the basic regeneration number greater than or less than 1 on the epidemic.