We present a compartmental mathematical model with demography for the spread of the COVID-19 disease, considering also asymptomatic infectious individuals. We compute the basic reproductive ratio of the model and study the local and global stability for it. We solve the model numerically based on the case of Italy. We propose a vaccination model and we derive threshold conditions for preventing infection spread in the case of imperfect vaccines.
The aim of this work is to investigate the optimal vaccine sharing between two SIR centers in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q=\int_0^{t_f}I(t){\rm d}t$ where $I(t)$ stands for the number of infectives at time $t$. We explain the behavior of the optimal allocation, which depends on the model parameters and the amount of available…
Several European countries have suspended the inoculation of the AstraZeneca vaccine out of suspicion of causing deep vein thrombosis. In this letter we report some Fermi estimates performed using a stochastic model aimed at making a risk-benefit analysis of the interruption of the delivery of the AstraZeneca vaccine in France and Italy. Our results clearly show that excess deaths due to the interruption of the vaccination campaign injections largely overrun those due to thrombosis even in worst case scenarios of frequency and gravity of the vaccine side effects.
During the COVID-19 outbreak, it is essential to monitor the effectiveness of measures taken by governments on the course of the epidemic. Here we show that there is already a sufficient amount of data collected in Italy to predict the outcome of the process. We show that using the proper metric, the data from Hubei Province and Italy has striking similarity, which enables us to calculate the expected number of confirmed cases and the number of deaths by the end of the process. Our predictions will improve as new data points are generated day by day, which can help to make further public decis…
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider that medical institutes may have limited vaccine resources available. In this manuscript, we explore the Susceptible-Infected-Recovered (SIR) model with local dynamic vaccination, and considering limited vaccines. In this model, susceptibles in contact with an infected individual, are vaccinated -with probability $ω$- and then get infected -with probability …
A great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of the ongoing COVID-19 pandemics. During the evolution of an outbreak, various non-pharmaceutical interventions are employed, the impact of which is frequently assessed by the reduction that they introduce to the effective reproduction number Rt; reduction below 1 is an indication of eventual dying out of the disease spread. Motivated by the fact that R0 essen…
Since early 2020, the world has been dealing with a raging pandemic outbreak: COVID-19. A year later, vaccines have become accessible, but in limited quantities, so that governments needed to devise a strategy to decide which part of the population to prioritize when assigning the available doses, and how to manage the interval between doses for multi-dose vaccines. In this paper, we present an optimization framework to address the dynamic double-dose vaccine allocation problem whereby the available vaccine doses must be administered to different age-groups to minimize specific societal object…
By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported, there is a light at the end of the tunnel. Several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than a million people over the world. On the other hand, there is growing evidence of re-infection by the virus, which can cause further outbreaks. In this paper, we apply statistical physics tools to examine the vaccination rate required to control the pandemic for three different vaccine efficien…
The rubeola virus, commonly known as measles, is one of the major causes of vaccine-preventable deaths among children worldwide. This is the case despite the fact that an effective vaccine is widely available. Even in developed countries elimination efforts have fallen short as seen by recent outbreaks in Europe, which had over 30,000 cases reported in 2010. The string of measles outbreaks in France from 2008-2011 is of particular interest due to the documented disparity in regional vaccination coverage. The impact of heterogeneous vaccine coverage on disease transmission is a broad interest a…
Analytical expressions for the basic reproduction number, R0, have been obtained in the past for a wide variety of mathematical models for infectious disease spread, along with expressions for the expected final size of an outbreak. However, what has so far not been studied is the average number of infections that descend down the chains of infection begun by each of the individuals infected in an outbreak (we refer to this quantity as the "average number of descendant infections" per infectious individual, or ANDI). ANDI includes not only the number of people that an individual directly conta…
The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of re…
This paper presents an dashboard developed to analyse the outbreak of the Covid-19 infection in Italy considering daily NUTS-3 data on positive cases provided by the Italian Ministry of Health and on deaths derived from Italian regional authorities' official press conferences. Descriptive time series plots are provided together with a map describing the spatial distribution of province cumulative cases and rates. A section on a proposed time-dependent adjusted SIRD model for NUTS-3 regions is also provided in the dashboard.
We propose a novel data-driven framework for assessing the a-priori epidemic risk of a geographical area and for identifying high-risk areas within a country. Our risk index is evaluated as a function of three different components: the hazard of the disease, the exposure of the area and the vulnerability of its inhabitants. As an application, we discuss the case of COVID-19 outbreak in Italy. We characterize each of the twenty Italian regions by using available historical data on air pollution, human mobility, winter temperature, housing concentration, health care density, population size and …
In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy. While virus transmission is ruled by a SEIAR type compartmental model, within our approach the population is given by a sum of commuters moving on a extra-urban scale and non commuters interacting only on the smaller urban scale. A transport dynamic of the commuter population at large spatial scales, based on kinetic equations, is coupled with a diffusion model for non commu…
In the night of February 20, 2020, the first case of novel coronavirus disease (COVID-19) was confirmed in the Lombardy Region, Italy. In the week that followed, Lombardy experienced a very rapid increase in the number of cases. We analyzed the first 5,830 laboratory-confirmed cases to provide the first epidemiological characterization of a COVID-19 outbreak in a Western Country. Epidemiological data were collected through standardized interviews of confirmed cases and their close contacts. We collected demographic backgrounds, dates of symptom onset, clinical features, respiratory tract speci…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors in reporting. Detailed epidemic models may contain a large number of empirical parameters, which cannot be determined with sufficient accuracy. In this paper, we show that the cumulative number of deaths can be regarded as a master variable, and the parameters of the epidemic such as the basic reproduction number, the size of the susceptible population, and …
West Nile virus outbreak in Italy modelled with the quantum Game of Life
Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）；INFN Napoli（意大利国家核物理研究所那不勒斯分部）；Università degli Studi di Palermo（巴勒莫大学）；Lobachevsky University of Nizhny Novgorod（下诺夫哥罗德罗巴切夫斯基大学）
The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can engender its own undoing if individuals choose to not get vaccinated in the belief that they are protected by herd immunity. Although this may appear to be an optimal decision, based on a rational appraisal of cost and benefits to the individual, it exposes the population to subsequent outbreaks. We investigate if voluntary vaccination can emerge in a an integra…
We discuss the generation of various reproduction ratios or numbers that are very useful to monitor an ongoing epidemic like Covid-19 and examine the effects of intervention measures. A detailed SEIR algorithm is described for their computation, with applications given to the current Covid-19 outbreaks in a number of countries (Argentina, Brazil, France, Italy, Mexico, Spain, UK and USA). The corresponding matlab script, complete and ready to use, is provided for free downloading.
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…
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…
Background: To prevent future outbreaks of COVID-19, Australia is pursuing a mass-vaccination approach in which a targeted group of the population comprising healthcare workers, aged-care residents and other individuals at increased risk of exposure will receive a highly effective priority vaccine. The rest of the population will instead have access to a less effective vaccine. Methods: We apply a large-scale agent-based model of COVID-19 in Australia to investigate the possible implications of this hybrid approach to mass-vaccination. The model is calibrated to recent epidemiological and demo…
Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of t…
Intent of this research is to explore how mathematical models, specifically Susceptible-Infected-Removed (SIR) model, can be utilized to forecast peak outbreak timeline of COVID-19 epidemic amongst a population of interest starting from the date of first reported case. Till the time of this research, there was no effective and universally accepted vaccine to control transmission and spread of this infection. COVID-19 primarily spreads in population through respiratory droplets from an infected person cough and sneeze which infects people who are in proximity. COVID-19 is spreading contagiously…
There are often multiple diseases with cross immunity competing for vaccination resources. Here we investigate the optimal vaccination program in a two-layer Susceptible-Infected-Removed (SIR) model, where two diseases with cross immunity spread in the same population, and vaccines for both diseases are available. We identify three scenarios of the optimal vaccination program, which prevents the outbreaks of both diseases at the minimum cost. We analytically derive a criterion to specify the optimal program based on the costs for different vaccines.
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in…
As of October 12, 2018, 211 cases of Ebola virus disease (EVD) were reported in North Kivu Province, Democratic Republic of Congo. Since the beginning of October the outbreak has largely shifted into regions in which active armed conflict is occurring, and in which EVD cases and their contacts are difficult for health workers to reach. We modeled EVD transmission using a branching process with gradually quenching transmission estimated from past EVD outbreaks, with outbreak trajectories conditioned on agreement with the course of the current outbreak, and with multiple levels of vaccination co…
During outbreaks of serious infectious diseases many individuals closely follow media reports of the outbreak and take steps, including self-isolation, to protect themselves from infection and possibly death. Self-isolation can take many forms including restricting local and long-distance travel, using face masks, and choosing to receive a vaccine. We use mathematical modeling to show that public health agencies working together with the media can significantly decrease the severity of an outbreak by providing timely and accurate accounts of the numbers of new infections and deaths. Our model …
COVID-19 in low-tolerance border quarantine systems: impact of the Delta variant of SARS-CoV-2
The University of Melbourne（墨尔本大学）；Melbourne School of Population and Global Health, The University of Melbourne（墨尔本大学人口与全球健康学院）；The Peter Doherty Institute for Infection and Immunity, The Royal Melbourne Hospital and The University of Melbourne（彼得·多赫蒂感染与免疫研究所、皇家墨尔本医院和墨尔本大学）；Department of Infectious Diseases, The Alfred and Central Clinical School, Monash University（莫纳什大学阿尔弗雷德医院和中央临床学院传染病系）；School of Mathematics and Statistics, The University of Melbourne（墨尔本大学数学与统计学院）
Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model i…
The impact of the outbreak of COVID-19 on health has been widely concerned. Disease risk assessment, prediction, and early warning have become a significant research field. Previous research suggests that there is a relationship between air quality and the disease. This paper investigated the impact of the atmospheric environment on the basic reproduction number (R$_0$) in Australia, South Korea, and Italy by using atmospheric environment data, confirmed case data, and the distributed lag non-linear model (DLNM) model based on Quasi-Poisson regression. The results show that the air temperature…
Background. The paper concerns the SARS-CoV2 (COVID-19) pandemic that, starting from the end of February 2020, began spreading along the Italian peninsula, by first attacking small communities in north regions, and then extending to the center and south of Italy, including the two main islands. Objective. The creation of a forecast model that manages to alert the decision-making bodies and, in particular, the healthcare system, to hinder the emergence of any other pandemic outbreaks, or the arrival of subsequent pandemic waves. Methods. A new mathematical model to describe the pandemic is give…
The current outbreak of novel coronavirus disease 2019 (COVID-19) poses an unprecedented global health and economic threat to interconnected human societies. Until a vaccine is developed, strategies for controlling the outbreak rely on aggressive social distancing. These measures largely disconnect the social network fabric of human societies, especially in urban areas. Here, we estimate the growth rates and reproductive numbers of COVID-19 in US cities from March 14th through March 19th to reveal a power-law scaling relationship to city population size. This means that COVID-19 is spreading f…
In this paper we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model for the analysis and forecast of the COVID-19 spread in some regions of Italy, using the data from the Italian Protezione Civile from February 24th 2020. In this study investigate an adaptation of the model. Since several restricting measures have been imposed by the Italian government at different times, starting from March 8th 2020, we propose a modification of SEIRD by introducing a time dependent transmitting rate. In the numerical results we report the maximum infection spread for the three I…
The spread of the coronavirus (COVID-19), starting in late 2019, has determined in Italy several interventions aimed to prevent saturation of the health system. We have examined the effects of such measures by proposing a mean-field model describing the spread of the infection based on a simple diffusion process where all the observable variables (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely diffusion coefficient, infection cross-section, and…
In late December 2019, a novel strand of Coronavirus (SARS-CoV-2) causing a severe, potentially fatal respiratory syndrome (COVID-19) was identified in Wuhan, Hubei Province, China and is causing outbreaks in multiple world countries, soon becoming a pandemic. Italy has now become the most hit country outside of Asia: on March 16, 2020, the Italian Civil Protection documented a total of 27980 confirmed cases and 2158 deaths of people tested positive for SARS-CoV-2. In the context of an emerging infectious disease outbreak, it is of paramount importance to predict the trend of the epidemic in o…
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
We have further extended our compartmental model describing the spread of the infection in Italy. The model is based on the assumption that the time evolution of all of the observable quantities (number of people still positive to the infection, hospitalized and fatalities cases, healed people, and total number of people that has contracted the infection) depend on average parameters, namely people diffusion coefficient, infection cross-section, and population density. The model provides precious information on the tight relationship between the variation of the reported infection cases and a …
SARS-CoV-2 is a severe respiratory infection that infects humans. Its outburst entitled it as a pandemic emergence. To get a grip on this, outbreak specific preventive and therapeutic interventions are urgently needed. It must be said that, until now, there are no existing vaccines for coronaviruses. To promptly and rapidly respond to pandemic events, the application of in silico trials can be used for designing and testing medicines against SARS-CoV-2 and speed-up the vaccine discovery pipeline, predicting any therapeutic failure and minimizing undesired effects. Here, we present an in silico…
Without vaccines and treatments, societies must rely on non-pharmaceutical intervention strategies to control the spread of emerging diseases such as COVID-19. Though complete lockdown is epidemiologically effective, because it eliminates infectious contacts, it comes with significant costs. Several recent studies have suggested that a plausible compromise strategy for minimizing epidemic risk is periodic closure, in which populations oscillate between wide-spread social restrictions and relaxation. However, no underlying theory has been proposed to predict and explain optimal closure periods …
The current COVID-19 pandemic is having detrimental consequences worldwide. The pandemic started to develop strongly by the end of January and beginning of February 2020, first in China with subsequent rapid spread to other countries with new epicenters of the outbreaks concentrated mainly within the 30-50 degrees North latitudinal band (e.g., South Korea, Japan, Iran, Italy, Spain). Simultaneously, an unusual persistent anticyclonic situation prevailing at latitudes around 40 degrees North was observed on global scale, in line with an anomalously strong positive phase of the Arctic Oscillatio…
The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new Biden administration is launching mass vaccination sites across the country, raising the obvious question of where to locate these clinics to maximize the effectiveness of the vaccination campaign. This paper tackles this question with a novel data-driven approach to optimize COVID-19 vaccine distribution. We first augment a sta…
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation (ODE) models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of a…
Understanding Covid-19 lethality and its variation from country to country is essential for supporting governments in the choice of appropriate strategies. Adopting correct indicators to monitor the lethality of the infection in the course of the outbreak is a crucial issue. This works highlights how far the time-dependent case fatality rate is a misleading indicator for estimating the fatality in the course of the outbreak, even if our attention is only restricted to the subset of confirmed cases. Our analysis proves that the final case fatality ratio for several major European countries is b…
The spatial propagation of many livestock infectious diseases critically depends on the animal movements among premises; so the knowledge of movement data may help us to detect, manage and control an outbreak. The identification of robust spreading features of the system is however hampered by the temporal dimension characterizing population interactions through movements. Traditional centrality measures do not provide relevant information as results strongly fluctuate in time and outbreak properties heavily depend on geotemporal initial conditions. By focusing on the case study of cattle disp…
The novel coronavirus SARS-CoV-2 and resulting COVID-19 disease have had an unprecedented spread and continue to cause an increasing number of fatalities worldwide. While vaccines are still under development, social distancing, extensive testing, and quarantining of confirmed infected subjects remain the most effective measures to contain the pandemic. These measures carry a significant socioeconomic cost. In this work, we introduce a novel optimization-based decision-making framework for managing the COVID-19 outbreak in the US. This includes modeling the dynamics of affected populations, est…
OBJECTIVES: to describe the first wave of the COVID-19 pandemic with a focus on undetected cases and to evaluate different post-lockdown scenarios. DESIGN: the study introduces a SEIR compartmental model, taking into account the region-specific fraction of undetected cases, the effects of mobility restrictions, and the personal protective measures adopted, such as wearing a mask and washing hands frequently. SETTING AND PARTICIPANTS: the model is experimentally validated with data of all the Italian regions, some European countries, and the US. MAIN OUTCOME MEASURES: the accuracy of the model …
The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources, such as the amount of infectious individuals. In this paper we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest, such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interacti…
Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detecte…
There is great interest in the dynamics of health behaviors in social networks and how they affect collective public health outcomes, but measuring population health behaviors over time and space requires substantial resources. Here, we use publicly available data from 101,853 users of online social media collected over a time period of almost six months to measure the spatio-temporal sentiment towards a new vaccine. We validated our approach by identifying a strong correlation between sentiments expressed online and CDC- estimated vaccination rates by region. Analysis of the network of opinio…
In the absence of neither an effective treatment or vaccine and with an incomplete understanding of the epidemiological cycle, Govt. has implemented a nationwide lockdown to reduce COVID-19 transmission in India. To study the effect of social distancing measure, we considered a new mathematical model on COVID-19 that incorporates lockdown effect. By validating our model to the data on notified cases from five different states and overall India, we estimated several epidemiologically important parameters as well as the basic reproduction number ($R_{0}$). Combining the mechanistic mathematical …
After the introduction of drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments have adopted a strategy based on a periodic relaxation of such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spread of the disease is an extremely difficult problem due to the many unknowns concerning the actual number of people infected, the actual reproduction number and infection fatality rate of the disease. In this work, starting from a compartmental mode…
This work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease. Differently from previous works we have considered continuous opinions. The epidemic spreading is governed by a SIS-like model with an extra vaccinated state. In our model individuals vaccinate with a probability proportional to their opinions. The opinions change due to peer influence in pairwise interactions. The epidemic feedback to the opinion dynamics acts as an…
