Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China.

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

FOREWORD Finding Balance in the Fight Against Gun Violence.

The United States is distinct among high-income countries for its problem with gun violence, with Americans 25 times more likely to be killed by gun homicide than people in other high-income countries.1 Suicides make up a majority of annual gun deaths - though that gap is closing as homicides are on the rise - and the U.S. accounts for 35% of global firearm suicides despite making up only 4% of the world's population.2 More concerning, gun deaths are only getting worse. In 2021, firearm fatalities approached 50,000, the highest we have seen in at least 40 years.3 The increase in homicides in conjunction with lower crime overall further suggests an problem specifically with guns.4 As devastating as these deaths are, it does not come close to encompassing the mass toll of America's gun violence epidemic - a toll that disproportionately impacts people of color, with the Black community suffering at the highest rates. A broader and more accurate view of what constitutes gun violence must become a part of the national discourse if we are going to develop effective strategies to combat this crisis.5.

Perfil das notificações de dengue e febre chikungunya em Cabo Frio/Rj, 2014-2019 / Profile of dengue and chikungunya notifications in Cabo Frio/Rj, 2014-2019 / Perfil de las notificaciones de dengue y chikungunya en Cabo Frio/Rj, 2014-2019

Introdução: De acordo com a literatura científica, diagnósticos clínicos diferenciais de arboviroses representam uma dificuldade no que tange à dengue, na medida em que está no Brasil há muitos anos, o que acarreta em ser a arbovirose mais conhecida no país. As notificações de arboviroses se tornaram obrigatórias para inserção no SINAN, possibilitando a construção de perfis demográficos e o cálculo de incidências a partir de informações específicas para estas doenças. No que tange à dengue, a epidemia deste agravo ocorre no país desde 1986, evidenciando falhas na prevenção, relacionadas a aspectos socioeconômicos e ambientais. Objetivo: analisar perfis das notificações de dengue e febre de chikungunya dos casos notificados no município de Cabo Frio. Metodologia: Trata-se de estudo transversal e descritivo, com uso de dados secundários do SINAN referentes a casos de arboviroses no município de Cabo Frio/RJ. Foram observadas variáveis relacionadas ao sexo, escolaridade, raça/cor e critérios de confirmação, além do grau de completude. Resultados: Foram notificados 8.777 casos suspeitos de arboviroses, incluindo-se 1.367 notificações (15,57%) referentes à febre de chikungunya e 1.986 (22,63%), à dengue. Em relação ao desfecho, 1186 casos (51,45%) foram fechados como inconclusivos e 344 destes (14,92%) foram descartados como arboviroses. Dentre os inconclusivos, 943 (79,51%) eram referentes à notificação de dengue, idem para os 277 casos descartados (80,52%). Conclusão: Observou-se baixa taxa de completude nas fichas de notificação, explicada pelo baixo número de recursos humanos e pela insuficiente infraestrutura. Sugere-se a interação de diferentes profissionais e pesquisadores, facilitando a compreensão da complexa dinâmica das arboviroses em questão.

Introduction: According to the scientific literature, differential clinical diagnoses of arboviruses represent a difficulty with regard to dengue, as it has been present in Brazil for many years, which makes it the most well-known arbovirus in the country. Notifications of arboviruses became mandatory for inclusion in SINAN, enabling the construction of demographic profiles and the calculation of incidences based on specific information for these diseases. With regard to dengue, the epidemic of this disease has occurred in the country since 1986, showing failures in prevention, related to socioeconomic and environmental aspects. Objective: to analyze profiles of notifications of dengue and chikungunya fever of cases notified in the municipality of Cabo Frio. Methodology: This is a cross-sectional and descriptive study, using secondary data from SINAN regarding cases of arboviruses in the municipality of Cabo Frio/RJ. Variables related to sex, education, race/color and confirmation criteria were observed, in addition to the degree of completeness. Results: 8,777 suspected cases of arboviruses were reported, including 1,367 reports (15.57%) referring to chikungunya fever and 1,986 (22.63%) to dengue fever. Regarding the outcome, 1186 cases (51.45%) were closed as inconclusive and 344 of these (14.92%) were discarded as arboviruses. Among the inconclusive ones, 943 (79.51%) were related to dengue notification, the same for the 277 discarded cases (80.52%). Conclusion: A low completeness rate was observed in the notification forms, explained by the low number of human resources and insufficient infrastructure. It is suggested the interaction of different professionals and researchers, facilitating the understanding of the complex dynamics of the arboviruses in question.

Introducción: Según la literatura científica, los diagnósticos clínicos diferenciales de los arbovirus representan una dificultad con respecto al dengue, ya que está presente en Brasil desde hace muchos años, lo que lo convierte en el arbovirus más conocido en el país. Las notificaciones de arbovirus pasaron a ser obligatorias para su inclusión en el SINAN, lo que permitió la construcción de perfiles demográficos y el cálculo de incidencias a partir de información específica de estas enfermedades. Con respecto al dengue, la epidemia de esta enfermedad se presenta en el país desde 1986, mostrando fallas en la prevención, relacionadas con aspectos socioeconómicos y ambientales. Objetivo: analizar perfiles de notificaciones de dengue y fiebre chikungunya de los casos notificados en el municipio de Cabo Frio. Metodología: Se trata de un estudio transversal y descriptivo, utilizando datos secundarios del SINAN sobre casos de arbovirus en el municipio de Cabo Frio/RJ. Se observaron variables relacionadas con el sexo, escolaridad, raza/color y criterios de confirmación, además del grado de completitud. Resultados: se notificaron 8.777 casos sospechosos de arbovirus, de los cuales 1.367 (15,57%) se referían a fiebre chikungunya y 1.986 (22,63%) a dengue. En cuanto al resultado, 1186 casos (51,45%) se cerraron como no concluyentes y 344 de estos (14,92%) se descartaron como arbovirus. Entre los inconclusos, 943 (79,51%) estaban relacionados con la notificación de dengue, lo mismo para los 277 casos descartados (80,52%). Conclusión: Se observó un bajo índice de completitud en los formularios de notificación, explicado por el bajo número de recursos humanos y la infraestructura insuficiente. Se sugiere la interacción de diferentes profesionales e investigadores, facilitando la comprensión de la compleja dinámica de los arbovirus en cuestión.

Effects of the information-driven awareness on epidemic spreading on multiplex networks.

In this study, we examine the impact of information-driven awareness on the spread of an epidemic from the perspective of resource allocation by comprehensively considering a series of realistic scenarios. A coupled awareness-resource-epidemic model on top of multiplex networks is proposed, and a Microscopic Markov Chain Approach is adopted to study the complex interplay among the processes. Through theoretical analysis, the infection density of the epidemic is predicted precisely, and an approximate epidemic threshold is derived. Combining both numerical calculations and extensive Monte Carlo simulations, the following conclusions are obtained. First, during a pandemic, the more active the resource support between individuals, the more effectively the disease can be controlled; that is, there is a smaller infection density and a larger epidemic threshold. Second, the disease can be better suppressed when individuals with small degrees are preferentially protected. In addition, there is a critical parameter of contact preference at which the effectiveness of disease control is the worst. Third, the inter-layer degree correlation has a "double-edged sword" effect on spreading dynamics. In other words, when there is a relatively lower infection rate, the epidemic threshold can be raised by increasing the positive correlation. By contrast, the infection density can be reduced by increasing the negative correlation. Finally, the infection density decreases when raising the relative weight of the global information, which indicates that global information about the epidemic state is more efficient for disease control than local information.

Assessing the Impacts of COVID-19 on the Industrial Sectors and Economy of China.

Since December 2019, the COVID-19 epidemic has been spreading continuously in China and many countries in the world, causing widespread concern among the whole society. To cope with the epidemic disaster, most provinces and cities in China have adopted prevention and control measures such as home isolation, blocking transportation, and extending the Spring Festival holiday, which has caused a serious impact on China's output of various sectors, international trade, and labor employment, ultimately generating great losses to the Chinese economic system in 2020. But how big is the loss? How can we assess this for a country? At present, there are few analyses based on quantitative models to answer these important questions. In the following, we describe a quantitative-based approach of assessing the potential impact of the COVID-19 epidemic on the economic system and the sectors taking China as the base case. The proposed approach can provide timely data and quantitative tools to support the complex decision-making process that government agencies (and the private sector) need to manage to respond to this tragic epidemic and maintain stable economic development. Based on the available data, this article proposes a hypothetical scenario and then adopts the Computable General Equilibrium (CGE) model to calculate the comprehensive economic losses of the epidemic from the aspects of the direct shock on the output of seriously affected sectors, international trade, and labor force. The empirical results show that assuming a GDP growth rate of 4-8% in the absence of COVID-19, GDP growth in 2020 would be -8.77 to -12.77% after the COVID-19. Companies and activities associated with transportation and service sectors are among the most impacted, and companies and supply chains related to the manufacturing subsector lead the economic losses. Finally, according to the calculation results, the corresponding countermeasures and suggestions are put forward: disaster recovery for key sectors such as the labor force, transportation sector, and service sectors should be enhanced; disaster emergency rescue work in highly sensitive sectors should be carried out; in the long run, precise measures to strengthen the refined management of disaster risk with big data resources and means should be taken.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves.

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Trends of maternal waterpipe, cigarettes, and dual tobacco smoking in Jordan. A decade of lost opportunities.

BACKGROUND: Maternal tobacco use is a global public health problem. In the literature, the focus was mainly on cigarette smoking, minimally on waterpipe use, and totally ignored dual use among pregnant women. We estimated the prevalence of current maternal tobacco use by tobacco product (cigarette, waterpipe, and dual use) over a period of ten years (2007 to 2017), and examined the socio-demographic patterning of maternal tobacco use. METHODS: A secondary analysis of Jordan DHS four data waves was conducted for women who reported to be pregnant at the time of the survey. Current cigarette and waterpipe tobacco use were investigated. Prevalence estimates for cigarette-only, waterpipe-only, and dual use, as well as for cigarette, regardless of waterpipe, and waterpipe, regardless of cigarette, were reported. The effect of independent variables on cigarette smoking, waterpipe use, and dual use was assessed. Logistic regression models assessed the adjusted effects of socio-demographic variables on cigarette smoking, waterpipe use, and on dual use. For each outcome variable, a time-adjusted and a time-unadjusted logistic models were conducted. RESULTS: Over the last decade, the prevalence estimates of current cigarette-only smoking slightly decreased. The prevalence estimates of current waterpipe-only use exceeded those for cigarette-only after 2007 and showed a steady overall increase. Current dual use showed a continuous rise especially after 2009. Gradual increase in cigarette smoking (4.1%, in 2007, and 5.7% in 2017) and in waterpipe use (2.5% to 6.4%) were detected. Education showed an inverse relationship with cigarette and waterpipe smoking. Household wealth demonstrated a positive association with cigarette and waterpipe smoking. CONCLUSIONS: Tobacco use epidemic is expanding its roots among pregnant women in Jordan through not only waterpipe use but also dual cigarette-waterpipe smoking. Maternal and child services should consider tobacco counseling and cessation.

Trends in opioid prescribing practices in South Korea, 2009-2019: Are we safe from an opioid epidemic?

Opioid prescribing data can guide regulation policy by informing trends and types of opioids prescribed and geographic variations. In South Korea, the nationwide data on prescribing opioids remain unclear. We aimed to evaluate an 11-year trend of opioid prescription in South Korea, both nationally and by administrative districts. A population-based cross-sectional analysis of opioid prescriptions dispensed nationwide in outpatient departments between January 1, 2009, and December 31, 2019, was conducted for this study. Data were obtained from the Health Insurance Review & Assessment Service. The types of opioids prescribed were categorized into total, strong, and extended-release and long-acting formulation. Trends in the prescription rate per 1000 persons were examined over time nationally and across administrative districts. There are significant increasing trends for total, strong, and extended-release and long-acting opioid prescriptions (rate per 1000 persons in 2009 and 2019: total opioids, 347.5 and 531.3; strong opioids, 0.6 and 15.2; extended-release and long-acting opioids, 6.8 and 82.0). The pattern of dispensing opioids increased from 2009 to 2013 and slowed down from 2013 to 2019. The rate of opioid prescriptions issued between administrative districts nearly doubled for all types of opioids. Prescription opioid dispensing increased substantially over the study period. The increase in the prescription of total opioids was largely attributed to an increase in the prescription of weak opioids. However, the increase in prescriptions of extended-release and long-acting opioids could be a future concern. These data may inform government organizations to create regulations and interventions for prescribing opioids.

Global dynamics of COVID-19 epidemic model with recessive infection and isolation.

In this paper, we present an SEIIaHR epidemic model to study the influence of recessive infection and isolation in the spread of COVID-19. We first prove that the infection-free equilibrium is globally asymptotically stable with condition R0<1 and the positive equilibrium is uniformly persistent when the condition R0>1. By using the COVID-19 data in India, we then give numerical simulations to illustrate our results and carry out some sensitivity analysis. We know that asymptomatic infections will affect the spread of the disease when the quarantine rate is within the range of [0.3519, 0.5411]. Furthermore, isolating people with symptoms is important to control and eliminate the disease.

Connectivity, reproduction number, and mobility interact to determine communities' epidemiological superspreader potential in a metapopulation network.

Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number (R). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R. We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R, centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R, alter host movements, or both.

Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation.

We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential equation with respect to a Poisson Random Measure (PRM), and how to simulate the process trajectory deterministically from a parameter value and a PRM realization. This forms the basis of our Data Augmented MCMC, which consists of augmenting parameter space with the unobserved PRM value. The resulting simple Metropolis-Hastings sampler acts as an efficient simulation-based inference method, that can easily be transferred from model to model. Compared with a recent Data Augmentation method based on Gibbs sampling of individual infection histories, PRM-augmented MCMC scales much better with epidemic size and is far more flexible. It is also found to be competitive with Particle MCMC for moderate epidemics when using approximate simulations. PRM-augmented MCMC also yields a posteriori estimates of the PRM, that represent process stochasticity, and which can be used to validate the model. A pattern of deviation from the PRM prior distribution will indicate that the model underfits the data and help to understand the cause. We illustrate this by fitting a non-seasonal model to some simulated seasonal case count data. Applied to the Zika epidemic of 2013 in French Polynesia, our approach shows that a simple SEIR model cannot correctly reproduce both the initial sharp increase in the number of cases as well as the final proportion of seropositive. PRM augmentation thus provides a coherent story for Stochastic Epidemic Model inference, where explicitly inferring process stochasticity helps with model validation.

Optimal periodic closure for minimizing risk in emerging disease outbreaks.

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 as a function of epidemiological and social parameters. In this work we develop such an analytical theory for SEIR-like model diseases, showing how characteristic closure periods emerge that minimize the total outbreak, and increase predictably with the reproductive number and incubation periods of a disease- as long as both are within predictable limits. Using our approach we demonstrate a sweet-spot effect in which optimal periodic closure is maximally effective for diseases with similar incubation and recovery periods. Our results compare well to numerical simulations, including in COVID-19 models where infectivity and recovery show significant variation.

Characterizing the type 2 diabetes mellitus epidemic in Jordan up to 2050.

We aimed to characterize the type 2 diabetes mellitus (T2DM) epidemic and the role of key risk factors in Jordan between 1990-2050, and to forecast the T2DM-related costs. A recently-developed population-level T2DM mathematical model was adapted and applied to Jordan. The model was fitted to six population-based survey data collected between 1990 and 2017. T2DM prevalence was 14.0% in 1990, and projected to be 16.0% in 2020, and 20.6% in 2050. The total predicted number of T2DM cases were 218,326 (12,313 were new cases) in 1990, 702,326 (36,941 were new cases) in 2020, and 1.9 million (79,419 were new cases) in 2050. Out of Jordan's total health expenditure, 19.0% in 1990, 21.1% in 2020, and 25.2% in 2050 was forecasted to be spent on T2DM. The proportion of T2DM incident cases attributed to obesity was 55.6% in 1990, 59.5% in 2020, and 62.6% in 2050. Meanwhile, the combined contribution of smoking and physical inactivity hovered around 5% between 1990 and 2050. Jordan's T2DM epidemic is predicted to grow sizably in the next three decades, driven by population ageing and high and increasing obesity levels. The national strategy to prevent T2DM needs to be strengthened by focusing it on preventive interventions targeting T2DM and key risk factors.

Initial Assessment of the Impact of the Emergency State Lockdown Measures on the 1st Wave of the COVID-19 Epidemic in Portugal.

INTRODUCTION: Portugal took early action to control the COVID-19 epidemic, initiating lockdown measures on March 16th when it recorded only 62 cases of COVID-19 per million inhabitants and reported no deaths. The Portuguese public complied quickly, reducing their overall mobility by 80%. The aim of this study was to estimate the initial impact of the lockdown in Portugal in terms of the reduction of the burden on the healthcare system. MATERIAL AND METHODS: We forecasted epidemic curves for: Cases, hospital inpatients (overall and in intensive care), and deaths without lockdown, assuming that the impact of containment measures would start 14 days after initial lockdown was implemented. We used exponential smoothing models for deaths, intensive care and hospitalizations and an ARIMA model for number of cases. Models were selected considering fitness to the observed data up to the 31st March 2020. We then compared observed (with intervention) and forecasted curves (without intervention). RESULTS: Between April 1st and April 15th, there were 146 fewer deaths (-25%), 5568 fewer cases (-23%) and, as of April 15th, there were 519 fewer intensive care inpatients (-69%) than forecasted without the lockdown. On April 15th, the number of intensive care inpatients could have reached 748, three times higher than the observed value (229) if the intervention had been delayed. DISCUSSION: If the lockdown had not been implemented in mid-March, Portugal intensive care capacity (528 beds) would have likely been breached during the first half of April. The lockdown seems to have been effective in reducing transmission of SARS-CoV-2, serious COVID-19 disease, and associated mortality, thus decreasing demand on health services. CONCLUSION: An early lockdown allowed time for the National Health Service to mobilize resources and acquire personal protective equipment, increase testing, contact tracing and hospital and intensive care capacity and to promote broad prevention and control measures. When lifting more stringent measures, strong surveillance and communication strategies that mobilize individual prevention efforts are necessary.

Introdução: Portugal tomou cedo medidas para controlar a epidemia de COVID-19, impondo medidas de confinamento a partir de 16 de março, quando registava apenas 62 casos de COVID-19 por milhão de habitantes e nenhuma morte. Os portugueses seguiram as recomendações reduzindo sua mobilidade em 80%. O objectivo deste estudo foi estimar o impacto do confinamento em Portugal com foco na redução do impacto nos serviço de saúde. Material e Métodos: Fizemos previsões para as curvas epidémicas de casos, internamento hospitalares (geral e em unidades de cuidados intensivos) e óbitos sem confinamento, assumindo que o impacto das medidas de contenção começaria 14 dias após o início das medidas. Utilizámos modelos de alisamento exponencial para óbitos, internados em cuidados intensivos e total de internados e um modelo ARIMA para número de novos casos. Os modelos foram selecionados considerando adequação aos dados observados até 31 de março de 2020. Em seguida, comparámos as curvas observadas (com intervenção) e previstas (sem intervenção). Resultados: Entre 1 e 15 de abril houve 146 menos mortes (-25%), 5568 menos casos (-23%) e, em 15 de abril, houve 519 menos internamentos em unidades de cuidados intensivos (-69%) e 508 menos doentes no total de internados (-28%) do que o previsto sem confinamento. Em 15 de abril, o número de pacientes internados na unidades de cuidados intensivos poderia ter atingido 748, três vezes maior que o valor observado (229) se a intervenção tivesse sido adiada. Discussão: Se o confinamento não tivesse sido implementado em meados de março, a capacidade de unidades de cuidados intensivos em Portugal (528 camas) teria provavelmente sido ultrapassada na primeira quinzena de abril. O confinamento parece ter sido eficaz na redução de infeções, doença grave e mortalidade associada, diminuindo a procura de serviços de saúde. Conclusão: Um confinamento antecipado permitiu comprar tempo para o Serviço Nacional de Saúde mobilizar recursos e adquirir equipamentos de proteção individual, aumentar a capacidade de testar e realizar rastreio de contactos, preparar-se para um aumento da procura hospitalar e de unidades de cuidados intensivos e promover amplas medidas de prevenção e controlo. Ao levantar medidas mais restritivas será importante manter uma vigilância epidemiológica e estratégias de comunicaçao robustas que mobilizem comportamentos individuais preventivos.

Current trends and future prediction of novel coronavirus disease (COVID-19) epidemic in China: a dynamical modeling analysis.

The novel coronavirus disease 2019 (COVID-19) infection broke out in December 2019 in Wuhan, and rapidly overspread 31 provinces in mainland China on 31 January 2020. In the face of the increasing number of daily confirmed infected cases, it has become a common concern and worthy of pondering when the infection will appear the turning points, what is the final size and when the infection would be ultimately controlled. Based on the current control measures, we proposed a dynamical transmission model with contact trace and quarantine and predicted the peak time and final size for daily confirmed infected cases by employing Markov Chain Monte Carlo algorithm. We estimate the basic reproductive number of COVID-19 is 5.78 (95%CI: 5.71-5.89). Under the current intervention before 31 January, the number of daily confirmed infected cases is expected to peak on around 11 February 2020 with the size of 4066 (95%CI: 3898-4472). The infection of COVID-19 might be controlled approximately after 18 May 2020. Reducing contact and increasing trace about the risk population are likely to be the present effective measures.

Disease and information spreading at different speeds in multiplex networks.

Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease-and its prevention methods-using the unaware-aware-unaware dynamics, so that informed individuals are less likely to be infected. Unlike previous related models where disease and information spread at the same time scale, we introduce here a parameter that controls the relative speed between the propagation of the two processes. We study the behavior of this model using a mean-field approach that gives results in good agreement with Monte Carlo simulations on homogeneous complex networks. We find that increasing the rate of information dissemination reduces the disease prevalence, as one may expect. However, increasing the speed of the information process as compared to that of the epidemic process has the counterintuitive effect of increasing the disease prevalence. This result opens an interesting discussion about the effects of information spreading on disease propagation.