A Novel Small-World Model: Using Social Mirror Identities for Epidemic Simulations

Abstract

The authors propose a small-world network model that combines cellular automata with the social mirror identities of daily-contact networks for purposes of performing epidemiological simulations. The social mirror identity concept was established to integrate human long-distance movement and daily visits to fixed locations. After showing that the model is capable of displaying such small-world effects as low degree of separation and relatively high degree of clustering on a societal level, the authors offer proof of its ability to display R0 properties—considered central to all epidemiological studies. To test their model, they simulated the 2003 severe acute respiratory syndrome (SARS) outbreak.

Epidemic simulation of a large-scale social contact network on GPU clusters

“…Individual-based network-oriented models emphasize on individual interactions and network structure. 1,3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Disease transmissions are only allowed between persons who have contacts. Over the last several years, it has been proved that network-based approaches are more useful for capturing complex contact patterns among individuals, exploring epidemic dynamics, and assessing the efficiencies of public health policies.…”

“…Large-scale, individual-based epidemiological models have been studied over the past few years, [1][2][3][4][5] which makes the social network, interaction based simulations 1,3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] proving successful for exploring epidemic dynamics and assessing intervention strategies among large and varied populations. They seek to develop detailed representation of the underlying social contact networks, within and across disease progression and transmission models, as well as computational representations of implementable policies.…”

Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis

“…A small world network can truly reflect the real social relationship between people. Afterwards, the issues related to social network are gradually based on the small world, such as, the spread of diseases, the transmission of the message and the network research of sexual relations and so on [11].…”

“…Also, if I ¼ 0, by the Lasalle invariance principle [11], we know that (7) limit set for each solution are contained in the largest set using concentration of {(S, E 1 , E 2 , I, T, V ) [ R + 6 |I = 0}, the second of (7) I ¼ 0 is clear, it is seen that when the time t 1, E 1 0, the third of (7) and E 1 0, it is seen that when the time t 1, E 2 0, Use the fifth of (7) and I ¼ 0, E 1 0 and E 2 0, it is obtained that when the time t 1, T 0, and then from the sixth of (7) when T 0, V V 0 , then the first of (7) and I ¼ 0 and V V 0 , it follows that when t 1, S S 0 , and via the largest invariant set {P 0 }, so P 0 is globally asymptotically stable.…”

“…(SEIR model is derived from the SIR model), [11] in this model N ¼ S + I + J + R, E is infected yet the disease is still latent. The number of asymptomatic, called latent; J indicates the number of confirmed cases, namely, the number of being diagnosed; S 1 and S 2 , are not vulnerable to infection and vulnerable to infection are not infected two people, respectively, S 2 is less susceptible to infected people, whose value is p; q is no symptoms yet having the potential proportion of contagious; k is the proportion of patients becoming latent, l for the isolation rate; a is the proportion for patients to be diagnosed and being diagnosed; the m is divided into two parts m 1 and m 2 ; m 1 expressed by the patient recovered as immunisation, the proportion, and m 2 is the proportion of immune persons recovered by the diagnosis; other parameters are the same as the previous model introduced and will not be detailed [15,16].…”