Epidemics with mutating infectivity on small-world networks

Taking cues from machine learning, compartmental and time series models for SARS-CoV-2 omicron infection in Indian provinces

SARS-CoV-2, the virus responsible for COVID-19, posed a significant threat to the world. We analyzed COVID-19 dissemination data in the top ten Indian provinces by infection incidences using the Susceptible-Infectious-Removed (SIR) model, an Autoregressive Integrated Moving Average (ARIMA) time series model, a machine learning model based on the Random Forest, and distribution fitting. Outbreaks are expected to continue if the Basic Reproduction Number (R0) > 1, and infection waves are anticipated to end if the R0 < 1, as determined by the SIR model. Different parametric probability distributions are also fitted. Data collected from December 12, 2021, to March 31, 2022, encompassing data from both before and during the implementation of strict control measures. Based on the estimates of the model parameters, health agencies and government policymakers can develop strategies to combat the spread of the disease in the future, and the most effective technique can be recommended for real-world application for other outbreaks of COVID-19. The best method out of these could be also implemented further on the epidemiological data of other similar infectious agents.

Network analysis of pig movement data as an epidemiological tool: an Austrian case study

Animal movements represent a major risk for the spread of infectious diseases in the domestic swine population. In this study, we adopted methods from social network analysis to explore pig trades in Austria. We used a dataset of daily records of swine movements covering the period 2015-2021. We analyzed the topology of the network and its structural changes over time, including seasonal and long-term variations in the pig production activities. Finally, we studied the temporal dynamics of the network community structure. Our findings show that the Austrian pig production was dominated by small-sized farms while spatial farm density was heterogeneous. The network exhibited a scale-free topology but was very sparse, suggesting a moderate impact of infectious disease outbreaks. However, two regions (Upper Austria and Styria) may present a higher structural vulnerability. The network also showed very high assortativity between holdings from the same federal state. Dynamic community detection revealed a stable behavior of the clusters. Yet trade communities did not correspond to sub-national administrative divisions and may be an alternative zoning approach to managing infectious diseases. Knowledge about the topology, contact patterns, and temporal dynamics of the pig trade network can support optimized risk-based disease control and surveillance strategies.

Minimizing the Spread of Negative Influence in SNIR Model by Contact Blocking

This paper presents a method to minimize the spread of negative influence on social networks by contact blocking. First, based on the infection-spreading process of COVID-19, the traditional susceptible, infectious, and recovered (SIR) propagation model is extended to the susceptible, non-symptomatic, infectious, and recovered (SNIR) model. Based on this model, we present a method to estimate the number of individuals infected by a virus at any given time. By calculating the reduction in the number of infected individuals after blocking contacts, the method selects the set of contacts to be blocked that can maximally reduce the affected range. The selection of contacts to be blocked is repeated until the number of isolated contacts that need to be blocked is reached or all infection sources are blocked. The experimental results on three real datasets and three synthetic datasets show that the algorithm obtains contact blockings that can achieve a larger reduction in the range of infection than other similar algorithms. This shows that the presented SNIR propagation model can more precisely reflect the diffusion and infection process of viruses in social networks, and can efficiently block virus infections.

Short- and Long-Range Connections Differentially Modulate the Dynamics and State of Small-World Networks

The human brain contains billions of neurons that flexibly interconnect to support local and global computational spans. As neuronal activity propagates through the neural medium, it approaches a critical state hedged between ordered and disordered system regimes. Recent work demonstrates that this criticality coincides with the small-world topology, a network arrangement that accommodates both local (subcritical) and global (supercritical) system properties. On one hand, operating near criticality is thought to offer several neurocomputational advantages, e.g., high-dynamic range, efficient information capacity, and information transfer fidelity. On the other hand, aberrations from the critical state have been linked to diverse pathologies of the brain, such as post-traumatic epileptiform seizures and disorders of consciousness. Modulation of brain activity, through neuromodulation, presents an attractive mode of treatment to alleviate such neurological disorders, but a tractable neural framework is needed to facilitate clinical progress. Using a variation on the generative small-world model of Watts and Strogatz and Kuramoto's model of coupled oscillators, we show that the topological and dynamical properties of the small-world network are divided into two functional domains based on the range of connectivity, and that these domains play distinct roles in shaping the behavior of the critical state. We demonstrate that short-range network connections shape the dynamics of the system, e.g., its volatility and metastability, whereas long-range connections drive the system state, e.g., a seizure. Together, these findings lend support to combinatorial neuromodulation approaches that synergistically normalize the system dynamic while mobilizing the system state.

Endogenous viral mutations, evolutionary selection, and containment policy design

How will the novel coronavirus evolve? I study a simple epidemiological model, in which mutations may change the properties of the virus and its associated disease stochastically and antigenic drifts allow new variants to partially evade immunity. I show analytically that variants with higher infectiousness, longer disease duration, and shorter latent period prove to be fitter. "Smart" containment policies targeting symptomatic individuals may redirect the evolution of the virus, as they give an edge to variants with a longer incubation period and a higher share of asymptomatic infections. Reduced mortality, on the other hand, does not per se prove to be an evolutionary advantage. I then implement this model as an agent-based simulation model in order to explore its aggregate dynamics. Monte Carlo simulations show that a) containment policy design has an impact on both speed and direction of viral evolution, b) the virus may circulate in the population indefinitely, provided that containment efforts are too relaxed and the propensity of the virus to escape immunity is high enough, and crucially c) that it may not be possible to distinguish between a slowly and a rapidly evolving virus by looking only at short-term epidemiological outcomes. Thus, what looks like a successful mitigation strategy in the short run, may prove to have devastating long-run effects. These results suggest that optimal containment policy must take the propensity of the virus to mutate and escape immunity into account, strengthening the case for genetic and antigenic surveillance even in the early stages of an epidemic.

COVID-19 related knowledge sharing practice and associated factors among healthcare providers worked in COVID-19 treatment centers at teaching hospitals in Northwest Ethiopia: A cross-sectional study

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Modelling Heterogeneity and Super Spreaders of the COVID-19 Spread through Malaysian Networks

Malaysia is multi-ethnic and diverse country. Heterogeneity, in terms of population interactions, is ingrained in the foundation of the country. Malaysian policies and social distancing measures are based on daily infections and R0 (average number of infections per infected person), estimated from the data. Models of the Malaysian COVID-19 spread are mostly based on the established SIR compartmental model and its variants. These models usually assume homogeneity and symmetrical full mixing in the population; thus, they are unable to capture super-spreading events which naturally occur due to heterogeneity. Moreover, studies have shown that when heterogeneity is present, R0 may be very different and even possibly misleading. The underlying spreading network is a crucial element, as it introduces heterogeneity for a more representative and realistic model of the spread through specific populations. Heterogeneity introduces more complexities in the modelling due to its asymmetrical nature of infection compared to the relatively symmetrical SIR compartmental model. This leads to a different way of calculating R0 and defining super-spreaders. Quantifying a super-spreader individual is related to the idea of importance in a network. The definition of a super-spreading individual depends on how super-spreading is defined. Even when the spreading is defined, it may not be clear that a single centrality always correlates with super-spreading, since centralities are network dependent. We proposed using a measure of super-spreading directly related to R0 and that will give a measure of ‘spreading’ regardless of the underlying network. We captured the vulnerability for varying degrees of heterogeneity and initial conditions by defining a measure to quantify the chances of epidemic spread in the simulations. We simulated the SIR spread on a real Malaysian network to illustrate the effects of this measure and heterogeneity on the number of infections. We also simulated super-spreading events (based on our definition) within the bounds of heterogeneity to demonstrate the effectiveness of the newly defined measure. We found that heterogeneity serves as a natural curve-flattening mechanism; therefore, the number of infections and R0 may be lower than expected. This may lead to a false sense of security, especially since heterogeneity makes the population vulnerable to super-spreading events.

Assessment of the Burden of SARS-CoV-2 Variants of Concern Among Essential Workers in the Greater Toronto Area, Canada

This cohort study examines the burden of SARS-CoV-2 variants of concern among frontline essential workers and by income in the City of Toronto and Region of Peel, Canada.

Small-world effects in a modified epidemiological model with mutation and permanent immune mechanism

Pandemic with mutation and permanent immune spreading in a small-world network described is studied by a modified SIR model, with consideration of mutation-immune mechanism. First, a novel mutation-immune model is proposed to modify the classical SIR model to simulate the transmission of mutable viruses that can be permanently immunized in small-world networks. Then, the influences of the size, coordination number and disorder parameter of the small-world network on the spread of the epidemic are analyzed in detail. Finally, the influences of mutation cycle and infection rate on epidemic transmission in small-world network are investigated further. The results show that the structure of the small-world network and the virus mutation cycle have an important impact on the spread of the epidemic. For viruses that can be permanently immunized, virus mutation is equivalent to making the immune cycle of human beings from infinite to finite. The dynamical behavior of the modified SIR epidemic model changes from an irregular, low-amplitude evolution at small disorder parameter to a spontaneous state of wide amplitude oscillations at large disorder parameter. Moreover, similar transition can also be found in increasing mutation cycle parameter. The maximum valid variation mutation decreases with the increase of disorder parameter and coordination number, but increase with respect to system size. In addition above, as the infection rate increases, the fraction of the infected increases and then decreases. As the mutation cycle increases, the time-average fraction of the infected and the infection rate corresponding to the maximum time-average fraction of the infected also decrease. As one conclusion, the results could give a deep understanding Pandemic with mutation and permanent immune spreading, from viewpoint of small-world network.

Simple mathematical models for controlling COVID-19 transmission through social distancing and community awareness

The novel COVID-19 pandemic is a current, major global health threat. Up till now, there is no fully approved pharmacological treatment or a vaccine. Also, its origin is still mysterious. In this study, simple mathematical models were employed to examine the dynamics of transmission and control of COVID-19 taking into consideration social distancing and community awareness. Both situations of homogeneous and nonhomogeneous population were considered. Based on the calculations, a sufficient degree of social distancing based on its reproductive ratio is found to be effective in controlling COVID-19, even in the absence of a vaccine. With a vaccine, social distancing minimizes the sufficient vaccination rate to control the disease. Community awareness also has a great impact in eradicating the virus transmission. The model is simulated on small-world networks and the role of social distancing in controlling the infection is explained.

Urban Fine-Grained Spatial Structure Detection Based on a New Traffic Flow Interaction Analysis Framework

The urban structure is the spatial reflection of various economic and cultural factors acting on the urban territory. Different from the physical structure, urban structure is closely related to the population mobility. Taxi trajectories are widely distributed, completely spontaneous, closely related to travel needs, and massive in data volume. Mining it not only can help us better understand the flow pattern of a city, but also provides a new perspective for interpreting the urban structure. On the basis of massive taxi trajectory data in Chengdu, we introduce a network science approach to analysis, propose a new framework for interaction analysis, and model the intrinsic connections within cities. The spatial grid of fine particles and the trajectory connections between them are used to resolve the urban structure. The results show that: (1) Based on 200,000 taxi trajectories, we constructed a spatial network of traffic flow using the interaction analysis framework and extracted the cold hot spots among them. (2) We divide the 400 traffic flow network nodes into 6 communities. Community 2 has high centrality and density, and belongs to the core built-up area of the city. (3) A traffic direction field is proposed to describe the direction of the traffic flow network, and the direction of traffic flow roughly presents an inflow from northeast to southwest and an outflow from southeast to northwest of the study area. The interaction analysis framework proposed in this study can be applied to other cities or other research areas (e.g., population migration), and it could extract the directional nature of the network as well as the hierarchical structure of the city.

A SIR model assumption for the spread of COVID-19 in different communities

In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by China, South Korea, India, Australia, USA, Italy and the state of Texas in the USA. The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot. Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions. Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures. We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020. By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.

Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic

In this paper, a susceptible-infected-removed (SIR) model has been used to track the evolution of the spread of COVID-19 in four countries of interest. In particular, the epidemic model, that depends on some basic characteristics, has been applied to model the evolution of the disease in Italy, India, South Korea and Iran. The economic, social and health consequences of the spread of the virus have been cataclysmic. Hence, it is imperative that mathematical models can be developed and used to compare published datasets with model predictions. The predictions estimated from the presented methodology can be used in both the qualitative and quantitative analysis of the spread. They give an insight into the spread of the virus that the published data alone cannot, by updating them and the model on a daily basis. We show that by doing so, it is possible to detect the early onset of secondary spikes in infections or the development of secondary waves. We considered data from March to August, 2020, when different communities were affected severely and demonstrate predictions depending on the model's parameters related to the spread of COVID-19 until the end of December, 2020. By comparing the published data with model results, we conclude that in this way, it may be possible to reflect better the success or failure of the adequate measures implemented by governments and authorities to mitigate and control the current pandemic.