Spatial spread of epidemic with Allee effect

Public health measures can effectively fight the epidemic in its initial phase, when the fraction of infected is not large. A common method is tracing the chains of infections and possibly quarantining people who were in close contact with infected individuals. This method leads to a reduction in the effective transmission rate; thus, it may stabilize the state of no infection to small perturbations. In population dynamics, this phenomenon is called an Allee effect, and it was recently proposed to be an important factor in the spread of epidemic. In this talk, I will consider the spatial spread of epidemic in the case of bistable dynamics, where the effective transmission rate depends on the fraction of infected, and the state of no epidemic is linearly stable. The front propagation phenomenon is investigated both numerically and theoretically, and a good agreement between numerical and theoretical results is found both for the front profiles and for the speed of invasion. We discovered [1] a novel phenomenon of front stoppage: in some regime of parameters, the front solution ceases to exist, and the propagating pulse of infection decays despite the initial outbreak.



[1]. E. Khain, Phys. Rev. E 107, 064303 (2023).