Where to cut to delay a pandemic with minimum disruption? mathematical analysis based on the SIS model

Abstract

We consider the problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers. We find an approximate solution to the Susceptible-Infected-Susceptible (SIS) model, which constitutes an upper bound to its exact solution. This upper bound allows direct structure-epidemic dynamic relations via the total communicability function. Using this approach we propose a strategy to remove edges in a network that significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers. We apply this strategy to the analysis of the UK airport transportation network weighted by the number of passengers transported in 2003. We find that the removal of all flights connecting four origin-destination pairs in the UK delays the propagation of a disease by more than 300%, with a minimal deterioration of the transportation capacity of this network. These time delays in the propagation of a disease represent an important non-pharmaceutical intervention to confront an epidemic, allowing for better preparations of the health systems, while keeping the economy moving with minimal disruptions.

Network bypasses sustain complexity

“…This expression is known as the communicability function of a graph ( 26 , 27 ). While originally being a purely combinatorial expression that encapsulates the contributions of different walks in a graph, indeed emerges as a central matrix when analyzing a wide variety of dynamics on graphs ( 27 – 31 ) (see SI Appendix , S1.1 for details and S1.2 for a derivation of as the actual propagator in a specific case with Hamiltonian dynamics). Nowadays communicability is applied across a range of disciplines, from neuroscience ( 32 – 39 ) or cancer research ( 40 ) to ecology ( 41 ) or economics ( 42 ), to cite a few.…”

Network bypasses sustain complexity

“…While originally being a purely combinatorial expression that encapsulate the contributions of different walks in a graph, G(β) indeed appears as a central matrix when analysing a wide variety of dynamics on graphs: in Hamiltonian dynamics, G(β) corresponds to the thermal Green's function of a network of coupled quantum harmonic oscillators [17], and similarly, the so-called self-communicability term G ii (β) quantifies the probability of finding a network, represented by a tight-binding Hamiltonian, in a state with energy E j = −λ j at inverse temperature β [18]. In the context of epidemic processes, G(β) appears in the solution of a linearised upper bound to the susceptible-infected (see SI S1.1) and susceptible-infectedsusceptible models [19,20]. G(β) has also been recently shown to be the the solution a modification of the Kuramoto model [21].…”

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

“…The problem of modifying a network topology in such a way as to delay the propagation of a disease with minimal disruption of the network capacity to reroute goods/items/passengers is considered here in 6 . A strategy is developed to remove edges in a network and it is shown that this significantly delays the propagation of a disease across the network with minimal disruption of its capacity to deliver goods/items/passengers.…”