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Register a new userTwo-level modeling of quarantine
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Evgeniy Khain
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Continuum models of epidemics do not take into account the underlying microscopic network structure of social connections. This drawback becomes extreme during quarantine when most people dramatically decrease their number of social interactions, while others (like cashiers in grocery stores) continue maintaining hundreds of contacts per day. We formulate a two-level model of quarantine. On a microscopic level, we model a single neighborhood assuming a star-network structure. On a mesoscopic level, the neighborhoods are placed on a two-dimensional lattice with nearest neighbors interactions. The modeling results are compared with the COVID-19 data for several counties in Michigan (USA) and the phase diagram of parameters is identified.
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The importance of a strict quarantine has been widely debated during the COVID-19 epidemic even from the purely epidemiological point of view. One argument against strict lockdown measures is that once the strict quarantine is lifted, the epidemic comes back, and so the cumulative number of infected individuals during the entire epidemic will stay the same. We consider an SIR model on a network and follow the disease dynamics, modeling the phases of quarantine by changing the node degree distribution. We show that the system reaches different steady states based on the history: the outcome of the epidemic is path-dependent despite the same final node degree distribution. The results indicate that two-phase route to the final node degree distribution (a strict phase followed by a soft phase) are always better than one phase (the same soft one) unless all the individuals have the same number of connections at the end (the same degree); in the latter case, the overall number of infected is indeed history-independent. The modeling also suggests that the optimal procedure of lifting the quarantine consists of releasing nodes in the order of their degree - highest first.
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We propose a minimal off-lattice model of living organisms where just a very few dynamical rules of growth are assumed. The stable coexistence of many clusters is detected when we replace the global restriction rule by a locally applied one. A rich variety of evolving patterns is revealed where players movement has a decisive role on the evolutionary outcome. For example, intensive individual mobility may jeopardize the survival of the population, but if we increase players movement further then it can save the population. Notably, the collective drive of population members is capable to compensate the negative consequence of intensive movement and keeps the system alive. When the drive becomes biased then the resulting unidirectional flow alters the stable pattern and produce a stripe-like state instead of the previously observed hexagonal arrangement of clusters. Interestingly, the rotation of stripes can be flipped if the individual movement exceeds a threshold value.
Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer networks and discuss in detail the main methods used to perform numerical simulations. Throughout the review, we classify spreading processes (disease and rumor models) into two classes according to the nature of time: (i) continuous-time and (ii) cellular automata approach, where the second one can be further divided into synchronous and asynchronous updating schemes. Our revision includes the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean field approaches, as well as their respective simulation techniques, emphasizing similarities and differences among the different techniques. The content presented here offers a whole suite of methods to study epidemic-like processes in complex networks, both for researchers without previous experience in the subject and for experts.
We introduce a minimalist dynamical model of wealth evolution and wealth sharing among $N$ agents as a platform to compare the relative merits of altruism and individualism. In our model, the wealth of each agent independently evolves by diffusion. For a population of altruists, whenever any agent reaches zero wealth (that is, the agent goes bankrupt), the remaining wealth of the other $N-1$ agents is equally shared among all. The population is collectively defined to be bankrupt when its total wealth falls below a specified small threshold value. For individualists, each time an agent goes bankrupt (s)he is considered to be dead and no wealth redistribution occurs. We determine the evolution of wealth in these two societies. Altruism leads to more global median wealth at early times; eventually, however, the longest-lived individualists accumulate most of the wealth and are richer and more long lived than the altruists.
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