Non-Markov stochastic dynamics of real epidemic process of respiratory infections

The study of social networks and especially of the stochastic dynamics of the diseases spread in human population has recently attracted considerable attention in statistical physics. In this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections (ARTI) by means of the theory of discrete non-Markov stochastic processes. We use the results of our last theory (Phys. Rev. E 65, 046107 (2002)) to study statistical memory effects, long - range correlation and discreteness in real data series, describing the epidemic dynamics of human ARTI infections and grippe. We have carried out the comparative analysis of the data of the two infections (grippe and ARTI) in one of the industrial districts of Kazan, one of the largest cities of Russia. The experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders, the phase portraits of the four first dynamic variables, the three first points of the statistical non-Markov parameter and the locally averaged kinetic and relaxation parameters. The received results give an opportunity to provide strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory. They also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network.Comment: 18 pages, 8figs, 1 table

Infection Curve Flattening via Targeted Interventions and Self-Isolation

Understanding the impact of network clustering and small-world properties on epidemic spread can be crucial in developing effective strategies for managing and controlling infectious diseases. Particularly in this work, we study the impact of these network features on targeted intervention (e.g., self-isolation and quarantine). The targeted individuals for self-isolation are based on centrality measures and node influence metrics. Compared to our previous works on scale-free networks, small-world networks are considered in this paper. Small-world networks resemble real-world social and human networks. In this type of network, most nodes are not directly connected but can be reached through a few intermediaries (known as the small-worldness property). Real social networks, such as friendship networks, also exhibit this small-worldness property, where most people are connected through a relatively small number of intermediaries. We particularly study the epidemic curve flattening by centrality-based interventions/isolation over small-world networks. Our results show that high clustering while having low small-worldness (higher shortest path characteristics) implies flatter infection curves. In reality, a flatter infection curve implies that the number of new cases of a disease is spread out over a longer period of time, rather than a sharp and sudden increase in cases (a peak in epidemic). In turn, this reduces the strain on healthcare resources and helps to relieve the healthcare services

Spread of Infectious Diseases with a Latent Period

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.Comment: 6 pages, 3 figure