Emergence of Persistent Infection due to Heterogeneity

Abstract

We explore the emergence of persistent infection in a closed region where the disease progression of the individuals is given by the SIRS model, with an individual becoming infected on contact with another infected individual. We investigate the persistence of contagion qualitatively and quantitatively, under increasing heterogeneity in the partitioning of the population into different disease compartments, as well as increasing heterogeneity in the phases of the disease among individuals within a compartment. We observe that when the initial population is uniform, consisting of individuals at the same stage of disease progression, infection arising from a contagious seed does not persist. However when the initial population consists of randomly distributed refractory and susceptible individuals, a single source of infection can lead to sustained infection in the population, as heterogeneity facilitates the de-synchronization of the phases in the disease cycle of the individuals. We also show how the average size of the window of persistence of infection depends on the degree of heterogeneity in the initial composition of the population. In particular, we show that the infection eventually dies out when the entire initial population is susceptible, while even a few susceptibles among an heterogeneous refractory population gives rise to a large persistent infected set.

Anticipating persistent infection

“…As mentioned before, one observes persistent infection (i.e. I = 0), in a window of I 0 [11]. Further, it is now clearly evident that in this same window of persistent infection, the global asymptotic synchronization order parameter is the lowest.…”

Localized spatial distributions of disease phases yield long-term persistence of infection

“…τ i , j ( t + 1) = 0. This signifies that after completion of the R stage the individual goes back to stage S. So the cellular automaton model of the cycle S → I → R → S is given concisely by the following update rules 25,27 :…”

“…We first recall the principal results for a single patch where the disease phases have a uniform random distribution 27 . Here persistent infection emerges only when the initial population consists of an admixture of susceptible and refractory individuals, and there is atleast one infectious seed.…”

“…In order to quantify the long-term persistence of disease we use a persistence order parameter 〈〈 I t 〉〉 defined in refs. 27,30 . This quantity is the fraction of infected individuals in the entire population, averaged over time of the order of several disease cycles (after long transients), and further averaged over a large sample of random initial conditions.…”

Sustained dynamics of a weakly excitable system with nonlocal interactions

“…Network connections of nonoscillatory elements, for instance, give rise to such dynamics and have been studied in various contexts, including gene networks [1], epidemic spreading dynamics [2][3][4][5], and generic excitable units [6][7][8][9][10], Excitable units undergo oscillations in many ways: Simple two excitable systems can exhibit sustained dynamics when delay-coupled [11]; spatially extended excitable media can produce sustained spiral waves by introducing a perturbation leading to the formation of a spiral core [12]; one can even consider interactions at a distance through nonlocal links embedded in spatially extended systems [13][14][15][16], which eventually forms network structures composed of wave propagation and nonlocal interactions.…”