We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents - poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and longer durations of intervention are found to progressively worsen outcomes for the poor; and these are of particular concern for economically vulnerable populations in cities of the developing world. Addressing these challenges requires a deeper, more rigorous understanding of the relationships between structural poverty and epidemy, as well as effective utilization of extant community level infrastructure for primary care in developing cities. Finally, improving iniquitous outcomes for the poor creates better outcomes for the whole population, including the non-poor.
Latin America is experiencing severe impacts of the SARS-CoV-2 pandemic, but poverty and weak public health institutions hamper gathering the kind of refined data needed to inform classical SEIR models of epidemics. We present an alternative approach that draws on advances in statistical ecology and conservation biology to enhance the value of sparse data in projecting and ameliorating epidemics. Our approach, leading to what we call a Stochastic Epidemic Gompertz model, with few parameters can flexibly incorporate heterogeneity in transmission within populations and across time. We demonstrat…
In this paper we present ACEMod, an agent-based modelling framework for studying influenza epidemics in Australia. The simulator is designed to analyse the spatiotemporal spread of contagion and influenza spatial synchrony across the nation. The individual-based epidemiological model accounts for mobility (worker and student commuting) patterns and human interactions derived from the 2006 Australian census and other national data sources. The high-precision simulation comprises 19.8 million stochastically generated software agents and traces the dynamics of influenza viral infection and transm…
We develop an agent-based model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the second through social contacts in public places: schools, hospitals, airports, etc., where many people meet, who live in remote geographic locations. Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks. We use…
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
In this paper, we present a model to predict the spread of the Covid-19 epidemic and apply it to the specific case of Italy. We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a certain time, the basic reproduction number $R_0$ exponentially decays in time, as empirically suggested by world data. Using this model, we were able to reproduce the real behavior of the epidemic with an average error of 5\%. Moreover, we illustrate possible future scenarios, associated to different intervals of $R_0$. This model has been used since the beginn…
Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introd…
Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system's behaviour. In this article we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the s…
Over the past two decades there has been a number of global outbreaks of viral diseases. This has accelerated the efforts to model and forecast the disease spreading, in order to find ways to confine the spreading regionally and between regions. Towards this we have devised a model of geographical spreading of viral infections due to human spatial mobility and adapted it to the latest COVID-19 pandemic. In this the region to be modelled is overlaid with a two-dimensional grid weighted with the population density defined cells, in each of which a compartmental SEIRS system of delay difference e…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from this framework offers an improvement over existing pair-based models by moving away from edge-centric descriptions while keeping the description concise and relatively simple. For the contagion process, we consider the Susceptible-Infected-Recovered (SIR) model, which is realized on a network with time-varying edges. We show that the shift in perspective from i…
A systematic review of COVID-19 epidemic models with endogenous human behaviour. What's next?
University of Pisa（比萨大学）；University of Florence（佛罗伦萨大学）；Bocconi University（博科尼大学）；University of Trieste（的里雅斯特大学）；Queen Mary University of London（伦敦大学玛丽女王学院）；University of Waterloo（滑铁卢大学）；IRTA-Leonardo, Istituto di Ricerca sul Territorio e l’Ambiente（领土与环境研究所（IRTA-Leonardo））
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a dual-layer static-dynamic multiplex network. The static network layer affords tunable clustering and describes an individual's permanent community structure. The dynamic network layer describes the transient connections an individual makes with members of the wider population by imposing constant edge rewiring. We follow the edge-based compartmental modelling app…
To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state attributes as living in and moving between the nodes of a graph, we use Monte-Carlo Markov Chain techniques to simulate the movements and health state changes of the individuals according to given probabilities of stay that have been preassigned to each of the nodes. We utilize this model to either capture and predict the future geographic evolution of an e…
Coronavirus COVID-19 spreads through the population mostly based on social contact. To gauge the potential for widespread contagion, to cope with associated uncertainty and to inform its mitigation, more accurate and robust modelling is centrally important for policy making. We provide a flexible modelling approach that increases the accuracy with which insights can be made. We use this to analyse different scenarios relevant to the COVID-19 situation in the UK. We present a stochastic model that captures the inherently probabilistic nature of contagion between population members. The computat…
A novel yet simple extension of the symmetric logistic distribution is proposed by introducing a skewness parameter. It is shown how the three parameters of the ensuing skew logistic distribution may be estimated using maximum likelihood. The skew logistic distribution is then extended to the skew bi-logistic distribution to allow the modelling of multiple waves in epidemic time series data. The proposed skew-logistic model is validated on COVID-19 data from the UK, and is evaluated for goodness-of-fit against the logistic and normal distributions using the recently formulated empirical surviv…
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process(2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao (2011). It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and co…
The coronavirus disease 2019 (COVID-19) pandemic has quickly become a global public health crisis unseen in recent years. It is known that the structure of the human contact network plays an important role in the spread of transmissible diseases. In this work, we study a structure aware model of COVID-19 CGEM. This model becomes similar to the classical compartment-based models in epidemiology if we assume the contact network is a Erdos-Renyi (ER) graph, i.e. everyone comes into contact with everyone else with the same probability. In contrast, CGEM is more expressive and allows for plugging i…
During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such behaviour has been obtained from 2020 late spring data coming from China by Ziff and Ziff in Ref. [1]. After this important observation the power-law scaling (albeit with different exponents) has also been observed in other countries during periods of containment of the spread. Early interpretations of these results suggest that this phenomenon might be due to spa…
Pandemics, in addition to affecting the health of populations, can have huge impacts on their social and economic behavior. These factors, on the other hand, have the potential to feed back to and influence the disease spreading. It is important to systematically study these interrelations, to determine which ones have significant effects, and whether the effects are adverse or beneficial. Our recently developed epidemic model with agent-based and geographical elements is used in this study for such a purpose. We perform an extensive parameter space exploration of the socio-economic part of th…
Using the classical Susceptible-Infected-Recovered epidemiological model, an analytical formula is derived for the number of beds occupied by Covid-19 patients. The analytical curve is fitted to data in Belgium, France, New York City and Switzerland, with a correlation coefficient exceeding 98.8%, suggesting that finer models are unnecessary with such macroscopic data. The fitting is used to extract estimates of the doubling time in the ascending phase of the epidemic, the mean recovery time and, for those who require medical intervention, the mean hospitalization time. Large variations can be…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One synthetic epidemic system with short range heterogeneous composition is modelled and its space-time evolution studied using maximum heterogeneity details. Two other modelling alternatives are applied, one of them using elementary mean-field variables, one other using non-localized geometrical parameters, so avoiding the limitations of the used mean-field model,…
The basic Susceptible-Infected-Recovered (SIR) model is extended to include effects of progressive social awareness, lockdowns and anthropogenic migration. It is found that social awareness can effectively contain the spread by lowering the basic reproduction rate $R_0$. Interestingly, the awareness is found to be more effective in a society which can adopt the awareness faster compared to the one having a slower response. The paper also separates the mortality fraction from the clinically recovered fraction and attempts to model the outcome of lockdowns, in absence and presence of social awar…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer si…
We review research papers which use game theory to model the decision making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. We show that the literature can be classified based on (i) type of population modelling (compartmental or network-based), (ii) frequency of the game (non-iterative or iterative), and (iii) type of strategy adoption (self-evaluation or imitation). We highlight that the choice of model depends on many factors such as the type of immunity the disease confers, the type of immunity the vaccine confers, a…
COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of va…
Mathematical modelling of the spread of epidemics has been an interesting challenge in the field of epidemiology. The SIR Model proposed by Kermack and McKendrick in 1927 is a prototypical model of epidemiology. However, it has its limitations. In this paper, we show two independent ways of generalizing this model, the first one if the vaccine isn't discovered or ready to use and the next one, if the vaccine is discovered and ready to use. In the first part, we have pointed out a major over-simplification, i.e., assumption of variation of the time derivatives of the variables with the linear o…
This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. This is done by an algorithm motivated by standard SIR models and aligned with the standard data provided by the Johns Hopkins University. To reconstruct data for the unregistered Infected, the algorithm uses current values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. Various examples of …
We examine the age-structured SIR model, a variant of the classical Susceptible-Infected-Recovered (SIR) model of epidemic propagation, in the context of COVID-19. In doing so, we provide a theoretical basis for the model, perform an empirical validation, and discover the limitations of the model in approximating arbitrary epidemics. We first establish the differential equations defining the age-structured SIR model as the mean-field limits of a continuous-time Markov process that models epidemic spreading on a social network involving random, asynchronous interactions. We then show that, as t…
Motivated by the need for novel robust approaches to modelling the Covid-19 epidemic, this paper treats a population of $N$ individuals as an inhomogeneous random social network (IRSN). The nodes of the network represent different types of individuals and the edges represent significant social relationships. An epidemic is pictured as a contagion process that changes daily, triggered on day $0$ by a seed infection introduced into the population. Individuals' social behaviour and health status are assumed to be random, with probability distributions that vary with their type. First a formulatio…
Infectious diseases are a threat for human health with tremendous impact on our society at large. The recent COVID-19 pandemic, caused by the SARS-CoV-2, is the latest example of a highly infectious disease ravaging the world, since late 2019. It is therefore imperative to develop efficient mathematical models, able to substantially curb the damages of a pandemic by unveiling disease spreading dynamics and symmetries. This will help inform (non)-pharmaceutical prevention strategies. For the reasons above we wrote this report that goes at the heart of mathematical modelling of infectious diseas…
