A network SIRX model for the spreading of COVID-19

Infectious diseases, such as the current COVID-19, have a huge economic and societal impact. The ability to model its transmission characteristics is critical to minimize its impact. In fact, predicting how fast an infection is spreading could be a major factor in deciding on the severity, extent and strictness of the applied mitigation measures, such as the recent lockdowns. Even though modelling epidemics is a well studied subject, usually models do not include quarantine or other social measures, such as those imposed in the recent pandemic. The current work builds upon a recent paper by Maier and Brockmann (2020), where a compartmental SIRX model was implemented. That model included social or individual behavioural changes during quarantine, by introducing state X , in which symptomatic quarantined individuals are not transmitting the infection anymore, and described well the transmission in the initial stages of the infection. The results of the model were applied to real data from several provinces in China, quite successfully. In our approach we use a Monte-Carlo simulation model on networks. Individuals are network nodes and the links are their contacts. We use a spreading mechanism from the initially infected nodes to their nearest neighbours, as has been done previously. Initially, we find the values of the rate constants (parameters) the same way as in Maier and Brockmann (2020) for the confirmed cases of a country, on a daily basis, as given by the Johns Hopkins University. We then use different types of networks (random Erdős-Rényi, Small World, and Barabási-Albert Scale-Free) with various characteristics in an effort to find the best fit with the real data for the same geographical regions as reported in Maier and Brockmann (2020). Our simulations show that the best fit comes with the Erdős-Rényi random networks. We then apply this method to several other countries, both for large-size countries, and small size ones. In all cases investigated we find the same result, i.e. best agreement for the evolution of the pandemic with time is for the Erdős-Rényi networks. Furthermore, our results indicate that the best fit occurs for a random network with an average degree of the order of 〈 k 〉 ≈ 10-25, for all countries tested. Scale Free and Small World networks fail to fit the real data convincingly.

Spontaneous repulsion in the A+B→0 reaction on coupled networks

We study the transient dynamics of an A+B→0 process on a pair of randomly coupled networks, where reactants are initially separated. We find that, for sufficiently small fractions q of cross couplings, the concentration of A (or B) particles decays linearly in a first stage and crosses over to a second linear decrease at a mixing time t_{x}. By numerical and analytical arguments, we show that for symmetric and homogeneous structures t_{x}∝(〈k〉/q)log(〈k〉/q) where 〈k〉 is the mean degree of both networks. Being this behavior is in marked contrast with a purely diffusive process, where the mixing time would go simply like 〈k〉/q, we identify the logarithmic slowing down in t_{x} to be the result of a spontaneous mechanism of repulsion between the reactants A and B due to the interactions taking place at the networks' interface. We show numerically how this spontaneous repulsion effect depends on the topology of the underlying networks.

Method for estimating critical exponents in percolation processes with low sampling

In phase-transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a large amount of realizations is needed to eliminate the noise in the data. In this paper, we introduce a novel method for the simultaneous estimation of the critical point p(c) and the critical exponent β/ν, applied for the case of "explosive" bond percolation on two-dimensional square lattices and Erdös-Rényi networks. The results show that with only a few hundred realizations, it is possible to acquire accurate values for these quantities. Guidelines are given at the end for the applicability of the method to other cases as well.

Percolation of randomly distributed growing clusters: finite-size scaling and critical exponents for the square lattice

We study the percolation properties of the growing clusters model on a 2D square lattice. In this model, a number of seeds placed on random locations on the lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration p and a second, nontrivial continuous phase transition for intermediate p values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.

[Intraoperative anaphylactic shock due to a latex allergy]

Delayed hypersensitivity to rubber chemicals is well known, but there has been an increasing number of reports of immediate-type hypersensitivity due to latex causing contact urticaria, angioedema, bronchial asthma, and anaphylactic shock in adults. We report a 10-year-old boy who developed anaphylactic shock during surgery due to surgical gloves containing latex. The patient was atopic and had a history of neurodermatitis and localized angioedema on exposure to rubber. There had been two previous uneventful surgical procedures. Thirty-five minutes after induction of anesthesia and 5 min after laparotomy for appendectomy there was an acute onset of increased airway pressure, oxygen desaturation, and profound hypotension. The circulation and gas exchange stabilized after treatment with oxygen, intravenous fluids, epinephrine, H1 and H2 blockers, aminophylline, and methylprednisolone. A positive skin test and RAST revealed a latex allergy. Latex can cause life-threatening allergic reactions in patients with a history of rubber allergy or frequent exposure to latex products.