A minimal model for multigroup adaptive SIS epidemics

TL;DR

This paper extends the adaptive NIMFA model to multigroup networks, analyzing disease spread with local and global awareness, revealing complex dynamics like periodic outbreaks and strategies for epidemic control.

Contribution

It introduces a multigroup aNIMFA model, provides stability analysis, and explores control strategies, demonstrating the model's applicability beyond SIS epidemics.

Findings

Periodic behavior can occur with two communities.

Breaking inter-community links is more effective for dense networks.

The model's adaptivity approach applies to various epidemiological models.

Abstract

We propose a generalization of the adaptive N-Intertwined Mean-Field Approximation (aNIMFA) model studied in Achterberg and Sensi (2023) to a heterogeneous network of communities. In particular, the multigroup aNIMFA model describes the impact of both local and global disease awareness on the spread of a disease in a network. We obtain results on existence and stability of the equilibria of the system, in terms of the basic reproduction number $R_0$. Assuming individuals have no reason to decrease their contacts in the absence of disease, we show that the basic reproduction number $R_0$ is equivalent to the basic reproduction number of the NIMFA model on static networks. Based on numerical simulations, we demonstrate that with just two communities periodic behaviour can occur, which contrasts the case with only a single community, in which periodicity was ruled out analytically. We also find that breaking connections between communities is more fruitful compared to breaking connections within communities to reduce the disease outbreak on dense networks, but both strategies are viable to networks with fewer links. Finally, we emphasize that our method of modelling adaptivity is not limited to SIS models, but has huge potential to be applied in other compartmental models in epidemiology.