Transmission Dynamics of a Two-City SIR Epidemic Model with Transport-Related Infections

A two-city SIR epidemic model with transport-related infections is proposed. Some good analytical results are given for this model. If the basic reproduction number ℜ0γ≤1, there exists a disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number ℜ0γ>1. We also show the permanence of this SIR model. In addition, sufficient conditions are established for global asymptotic stability of the endemic equilibrium

Exploring the role of spatial configuration and behavior on the spread of the epidemic: A study of factors that affect Covid-19 spreading in the city

This research explores how exterior public space - defined through the configuration of the city - and human behavior affect the spread of disease. In order to understand the virus spreading mechanism and influencing factors of the epidemic which accompany residents' movement, this study attempts to reproduce the process of virus spreading in city areas through computer simulation. The simulation can be divided into residents' movement simulation and the virus spreading simulation. First, the Agent-based model (ABM) can effectively simulate the behavior of the individual and crowd;real location data - uploaded by residents via mobile phone applications - is used as a behavioral driving force for the agent's movement. Second, a mathematical model of infectious diseases is constructed based on SIR (SEIR) Compartmental models in epidemiology. Finally, by analyzing the simulation results of the agent's movement in the city and the virus spreading under different conditions, the influence of multiple factors of city configuration and human behavior on the virus spreading process is explored, and the effectiveness of countermeasures such as social distancing and lockdown are further demonstrated

Social Interaction Layers in Complex Networks for the Dynamical Epidemic Modeling of COVID-19 in Brazil

We are currently living in a state of uncertainty due to the pandemic caused by the Sars-CoV-2 virus. There are several factors involved in the epidemic spreading such as the individual characteristics of each city/country. The true shape of the epidemic dynamics is a large, complex system such as most of the social systems. In this context, Complex networks are a great candidate to analyze these systems due to their ability to tackle structural and dynamical properties. Therefore this study presents a new approach to model the COVID-19 epidemic using a multi-layer complex network, where nodes represent people, edges are social contacts, and layers represent different social activities. The model improves the traditional SIR and it is applied to study the Brazilian epidemic by analyzing possible future actions and their consequences. The network is characterized using statistics of infection, death, and hospitalization time. To simulate isolation, social distancing, or precautionary measures we remove layers and/or reduce the intensity of social contacts. Results show that even taking various optimistic assumptions, the current isolation levels in Brazil still may lead to a critical scenario for the healthcare system and a considerable death toll (average of 149,000). If all activities return to normal, the epidemic growth may suffer a steep increase, and the demand for ICU beds may surpass 3 times the country's capacity. This would surely lead to a catastrophic scenario, as our estimation reaches an average of 212,000 deaths even considering that all cases are effectively treated. The increase of isolation (up to a lockdown) shows to be the best option to keep the situation under the healthcare system capacity, aside from ensuring a faster decrease of new case occurrences (months of difference), and a significantly smaller death toll (average of 87,000).Comment: 16 pages, 7 figures, 2 table

Networks and the epidemiology of infectious disease

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues

Modeling and simulation for the spread of Covid-19 in an Indian city: a case study

We present a case study on modeling and predicting the course of Covid-19 in the Indian city of Pune. The results presented in this paper are concerned primarily with the wave of infections triggered by the Delta variant during the period between February and June 2021. Our work demonstrates the necessity for bringing together compartmental stock-and-flow and agent-based models and the limitations of each approach when used individually. Some of the work presented here was carried out in the process of advising the local city administration and reflects the challenges associated with employing these models in a real-world environment with its uncertainties and time pressures. Our experience, described in the paper, also highlights the risks associated with forecasting the course of an epidemic with evolving variants

Agent based simulators for Covid-19: Simulating larger models using smaller ones

Agent-based simulators (ABS) are a popular epidemiological modelling tool to study the impact of various non-pharmaceutical interventions in managing an epidemic in a city. They provide the flexibility to accurately model a heterogeneous population with time and location varying, person-specific interactions. Government policies such as localised lockdowns, case isolation, home quarantine etc. and important pandemic developments including presence of variants as well as vaccines, are easily incorporated in an ABS. Typically, for accuracy, each person is modelled separately. This however may make computational time prohibitive when the city population and the simulated time is large. In this paper, we primarily focus on the COVID-19 pandemic and dig deeper into the underlying probabilistic structure of a generic ABS to arrive at modifications that allow smaller models to give accurate statistics for larger ones. We observe that simply considering a smaller aggregate model and scaling up the output leads to inaccuracies. We exploit the observation that in the initial Covid spread phase, the starting infections create a family tree of infected individuals more-or-less independent of the other trees and are modelled well as a multi-type super-critical branching process. Further, the relative proportions amongst the population types stabilises quickly. Soon after, for large city population, once enough people have been infected, the future evolution of the pandemic is closely approximated by its mean field limit with a random starting state. We build upon these insights to develop a shifted, scaled and restart based algorithm that accurately evaluates the ABS's performance using a much smaller model while carefully reducing the bias that may otherwise arise. We theoretically support the proposed algorithm through an asymptotic analysis where the population size increases to infinity.Comment: 33 pages, 13 figures, 6 table