Forecast of omicron wave time evolution

Adopting an early doubling time of three days for the rate of new infections with the omicron mutant the temporal evolution of the omicron wave in different countries is predicted. The predictions are based on the susceptible-infectious-recovered/removed (SIR) epidemic compartment model with a constant stationary ratio k=mu(t)/a(t) between the infection (a(t)) and recovery (mu(t)) rate. The fixed early doubling time then uniquely relates the initial infection rate a0 to the ratio k, which therefore determines the full temporal evolution of the omicron waves. For each country three scenarios (optimistic, pessimistic, intermediate) are considered and the resulting pandemic parameters are calculated. These include the total number of infected persons, the maximum rate of new infections, the peak time and the maximum 7-day incidence per 100000 persons. Among the considered European countries Denmark has the smallest omicron peak time and the recently observed saturation of the 7-day incidence value at 2478 is in excellent agreement with the prediction in the optimistic scenario. For Germany we predict peak times of the omicron wave ranging from 32 to 38 and 45 days after the start of the omicron wave in the optimistic, intermediate and pessimistic scenario, respectively, with corresponding maximum SDI values of 7090, 13263 and 28911, respectively. Adopting Jan 1st, 2022 as the starting date our predictions implies that the maximum of the omicron wave is reached between Feb 1 and Feb 15, 2022. Rather similar values are predicted for Switzerland. Due to an order of magnitude smaller omicron hospitalization rate, due to the high percentage of vaccinated and boostered population, the German health system can cope with maximum omicron SDI value of 2800 which is about a factor 2.5 smaller than the maximum omicron SDI value 7090 in the optimistic case. By either reducing the duration of intensive care during this period of maximum, and/or by making use of the nonuniform spread of the omicron wave across Germany, it seems that the German health system can barely cope with the omicron wave avoiding triage decisions. The reduced omicron hospitalization rate also causes significantly smaller mortality rates compared to the earlier mutants in Germany. In the optimistic scenario one obtains for the total number of fatalities 7445 and for the maximum death rate 418 per day which are about one order of magnitude smaller than the beta fatality rate and total number.

The impact of spatial and social structure on an SIR epidemic on a weighted multilayer network

A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

Mitigate SIR epidemic spreading via contact blocking in temporal networks

Progress has been made in how to suppress epidemic spreading on temporal networks via blocking all contacts of targeted nodes or node pairs. In this work, we develop contact blocking strategies that remove a fraction of contacts from a temporal (time evolving) human contact network to mitigate the spread of a Susceptible-Infected-Recovered epidemic. We define the probability that a contact c(i, j, t) is removed as a function of a given centrality metric of the corresponding link l(i, j) in the aggregated network and the time t of the contact. The aggregated network captures the number of contacts between each node pair. A set of 12 link centrality metrics have been proposed and each centrality metric leads to a unique contact removal strategy. These strategies together with a baseline strategy (random removal) are evaluated in empirical contact networks via the average prevalence, the peak prevalence and the time to reach the peak prevalence. We find that the epidemic spreading can be mitigated the best when contacts between node pairs that have fewer contacts and early contacts are more likely to be removed. A strategy tends to perform better when the average number contacts removed from each node pair varies less. The aggregated pruned network resulted from the best contact removal strategy tends to have a large largest eigenvalue, a large modularity and probably a small largest connected component size.

Global dynamics for a class of reaction–diffusion multigroup SIR epidemic models with time fractional-order derivatives

This paper investigates the global dynamics for a class of multigroup SIR epidemic model with time fractional-order derivatives and reaction–diffusion. The fractional order considered in this paper is in (0; 1], which the propagation speed of this process is slower than Brownian motion leading to anomalous subdiffusion. Furthermore, the generalized incidence function is considered so that the data itself can flexibly determine the functional form of incidence rates in practice. Firstly, the existence, nonnegativity, and ultimate boundedness of the solution for the proposed system are studied. Moreover, the basic reproduction number R0 is calculated and shown as a threshold: the disease-free equilibrium point of the proposed system is globally asymptotically stable when R0 ≤ 1, while when R0 > 1, the proposed system is uniformly persistent, and the endemic equilibrium point is globally asymptotically stable. Finally, the theoretical results are verified by numerical simulation.