(University College London)
Stability criteria for multi-city epidemic models
Absztrakt: We describe a new approach for investigating the control strategies of compartmental disease transmission models. The method rests on the construction of various alternative next-generation matrices, and uses the concept of the target reproduction number. The application of the method will be first illustrated on a general SIRS (susceptible–infected–recovered–susceptible) model when the population is distributed over different cities that are connected by instantaneous travel. Considering various control measures such as social distancing and travel restrictions, the new method allows us to precisely describe in terms of the model parameters, how control methods should be implemented in the SIRS model to ensure disease elimination. We show that the method can also be used to derive stability conditions for the disease-free equilibrium in terms of various model parameters. Lastly, an SIRS-based functional-differential model will also be presented that incorporates travel time between the different cities (hence the delay in the underlying system) and travel-related infections. We will give necessary and sufficient condition for the stability of the disease-free equilibrium, and apply the method described in the first part of the talk to give stability threshold in terms of the delays.