The mathematical interpretation of interventions for the mitigation of epidemics and pandemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of infections to manage impact. Whilst these methods may work in theory, in order to implement they may require information which is likely not available whilst one is in the midst of an epidemic, or they may require impeccable data about infection levels in the community. In practice, testing and cases data is only as good as the policy of implementation and the compliance of the individuals, which means that understanding the levels of infections becomes difficult or complicated from the data that is provided. In this paper, we aim to develop a different approach to the mathematical modelling of interventions, not based on optimality, but based on demand and capacity of local authorities who have to deal with the epidemic on a day to day basis. In particular, we use data-driven modelling to calibrate an Susceptible Exposed Infectious Recovered-Died (SEIR-D) model to infer parameters that depict the dynamics of the epidemic in a region of the UK. We use the calibrated parameters for forecasting scenarios and understand, given a maximum capacity of hospital healthcare services, how the timing of interventions, severity of interventions, and conditions for the releasing of interventions affect the overall epidemic-picture.
Measures to reduce the impact of the COVID-19 pandemic require a mix of logistic, political and social capacity. Depending on the country, different approaches to increase hospitalization capacity or to properly apply lock-downs are observed. In order to better understand the impact of these measures we have developed a compartmental model which, on the one hand allows to calibrate the reduction of movement of people within and among different areas, and on the other hand it incorporates a hospitalization dynamics that differentiates the available kinds of treatment that infected people can re…
The transmission of COVID-19 is dependent on social contacts, the rate of which have varied during the pandemic due to mandated and voluntary social distancing. Changes in transmission dynamics eventually affect hospital admissions and we have used this connection in order to model and predict regional hospital admissions in Sweden during the COVID-19 pandemic. We use an SEIR-model for each region in Sweden in which the infectivity is assumed to depend on mobility data in terms of public transport utilisation and mobile phone usage. The results show that the model can capture the timing of the…
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…
We propose a new mathematical model to study the coinfection dynamics of COVID-19 and bacterial pneumonia. Our model includes two infection ways for pneumonia, corresponding to community-acquired and hospital-acquired infections. We show that the existence and local stability of equilibria depend on three different parameters, which are interpreted as the basic reproduction numbers of COVID-19, bacterial pneumonia, and bacterial population. Numerical simulations are performed to complement our theoretical analysis, and we show that both diseases can persist if the basic reproduction number of …
We present a compartmental SEIRD model aimed at forecasting hospital occupancy in metropolitan areas during the current COVID-19 outbreak. The model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non exponential residence times in each latent and infected compartments. Using both hospital admittance confirmed cases and deaths we infer the contact rate and the initial conditions of the dynamical system, considering break points to model lockdown interventions. Our Bayesian approach allows us to produce timely pro…
There are several reports in India that indicate hospitals and quarantined centers are COVID-19 hotspots. In the absence of efficient contact tracing tools, Govt. and the policymakers may not be paying attention to the risk of hospital-based transmission. To explore more on this important route and its possible impact on lockdown effect, we developed a mechanistic model with hospital-based transmission. Using daily notified COVID-19 cases from six states (Maharashtra, Delhi, Madhya Pradesh, Rajasthan, Gujarat, and Uttar Pradesh) and overall India, we estimated several important parameters of t…
The first year of the COVID-19 pandemic put considerable strain on the national healthcare system in England. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, which was coupled to a model of the generalised epidemic. We named this model EpiBeds. Data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds …
Knowing COVID-19 epidemiological distributions, such as the time from patient admission to death, is directly relevant to effective primary and secondary care planning, and moreover, the mathematical modelling of the pandemic generally. We determine epidemiological distributions for patients hospitalised with COVID-19 using a large dataset ($N=21{,}000-157{,}000$) from the Brazilian Sistema de Informação de Vigilância Epidemiológica da Gripe database. A joint Bayesian subnational model with partial pooling is used to simultaneously describe the 26 states and one federal district of Brazil, and…
The COVID-19 pandemic has rapidly spread around the world and burdened public health in almost all countries involving France. After the spread of SARS-CoV-2, France harvested many deaths in total. In this paper, we develop models with integer and fractional orders to investigate the dynamics of COVID-19 transmission in French hospitals and intensive care units (ICUs). Moreover, this paper aims to explore the impact of precautionary measures on the total infected cases in hospitals and ICUs of COVID-19 for the entire France by using available actual data.
We assess the impact of COVID-19 response measures implemented in Germany and Switzerland on cumulative COVID-19-related hospitalization and death rates. Our analysis exploits the fact that the epidemic was more advanced in some regions than in others when certain lockdown measures came into force, based on measuring health outcomes relative to the region-specific start of the epidemic and comparing outcomes across regions with earlier and later start dates. When estimating the effect of the relative timing of measures, we control for regional characteristics and initial epidemic trends by lin…
The aim of this study is to propose a modified Susceptible-Exposed-Infectious-Removed (SEIR) model that describes the behaviour of symptomatic, asymptomatic and hospitalized patients of COVID-19 epidemic, including the effect of demographic variation of population. It is shown that considering a population growth proportional to the total population leads to solutions with a qualitative behaviour different from the behaviour obtained in many studies, where constant growth ratio is assumed. An exhaustive theoretical study is carried out and the basic reproduction number $R_0$ is computed from t…
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…
Bareilly College（巴雷利学院）；CSIR-Central Electronics Engineering Research Institute（CSIR-中央电子工程研究所）；Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学）
To combat the coronavirus disease 2019 (COVID-19) pandemic, the world has vaccination, plasma therapy, herd immunity, and epidemiological interventions as few possible options. The COVID-19 vaccine development is underway and it may take a significant amount of time to develop the vaccine and after development, it will take time to vaccinate the entire population, and plasma therapy has some limitations. Herd immunity can be a plausible option to fight COVID-19 for small countries. But for a country with huge population like India, herd immunity is not a plausible option, because to acquire he…
Background: By the beginning of December 2020, some vaccines against COVID-19 already presented efficacy and security, which qualify them to be used in mass vaccination campaigns. Thus, setting up strategies of vaccination became crucial to control the COVID19 pandemic. Methods: We use daily COVID-19 reports from Chicago and NYC from 01-Mar2020 to 28- Nov-2020 to estimate the parameters of an SEIR-like epidemiological model that accounts for different severity levels. To achieve data adherent predictions, we let the model parameters to be time-dependent. The model is used to forecast different…
A Mathematical Model of Dengue Transmission Incorporating Hospital Capacity and Threshold-Based Fogging Interventions
Universitas Indonesia（印度尼西亚大学）；Escuela Superior Politécnica del Litoral（沿海高等理工学院）；TU Dresden（德累斯顿工业大学）；Ordu University（奥尔杜大学）；University of Koblenz（科布伦茨大学）；Johannes–Gutenberg Universität Mainz（约翰内斯·古腾堡美因茨大学）；Institute for Quantitative and Computational Biosciences (IQCB), Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学定量与计算生物科学研究所）
We present a compartmental meta-population model for the spread of Covid-19 in India. Our model simulates populations at a district or state level using an epidemiological model that is appropriate to Covid-19. Different districts are connected by a transportation matrix developed using available census data. We introduce uncertainties in the testing rates into the model that takes into account the disparate responses of the different states to the epidemic and also factors in the state of the public healthcare system. Our model allows us to generate qualitative projections of Covid-19 spread …
Motivated by COVID-19, we develop and analyze a simple stochastic model for a disease spread in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening the society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown o…
The SIR evolutionary model predicts too sharp a decrease of the fractions of people infected with COVID-19 in France after the start of the national lockdown, compared to what is observed. I fit the daily hospital data: arrivals in regular and critical care units, releases and deaths, using extended SEIR models. These involve ratios of evolutionary timescales to branching fractions, assumed uniform throughout a country, and the basic reproduction number, $R_0$, before and during the national lockdown, for each region of France. The joint-region Bayesian analysis allows precise evaluations of t…
The pandemic of COVID-19 has caused severe public health consequences around the world. Many interventions of COVID-19 have been implemented. It is of great public health and societal importance to evaluate the effects of interventions in the pandemic of COVID-19. In this paper, with help of synthetic control method, regression discontinuity and a Susceptible-Infected and infectious without isolation-Hospitalized in isolation-Removed (SIHR) model, we evaluate the horizontal and longitudinal effects of stringent interventions implemented in Wenzhou, a representative urban city of China, where s…
This paper introduces a dynamic panel SIR (DP-SIR) model to investigate the impact of non-pharmaceutical interventions (NPIs) on the COVID-19 transmission dynamics with panel data from 9 countries across the globe. By constructing scenarios with different combinations of NPIs, our empirical findings suggest that countries may avoid the lockdown policy with imposing school closure, mask wearing and centralized quarantine to reach similar outcomes on controlling the COVID-19 infection. Our results also suggest that, as of April 4th, 2020, certain countries such as the U.S. and Singapore may requ…
An epidemiological compartmental model was used to simulate social distancing strategies to contain the COVID-19 pandemic and prevent a second wave in Sao Paulo, Brazil. Optimization using genetic algorithm was used to determine the optimal solutions. Our results suggest the best-case strategy for Sao Paulo is to maintain or increase the current magnitude of social distancing for at least 60 more days and increase the current levels of personal protection behaviors by a minimum of 10% (e.g., wearing facemasks, proper hand hygiene and avoid agglomeration). Followed by a long-term oscillatory le…
Epidemic models play a key role in understanding and responding to the emerging COVID-19 pandemic. Widely used compartmental models are static and are of limited use to evaluate intervention strategies with the emerging pandemic. Applying the technology of data assimilation, we propose a Bayesian updating approach for estimating epidemiological parameters using observable information for the purpose of assessing the impacts of different intervention strategies. We adopt a concise renewal model and propose new parameters by disentangling the reduction of instantaneous reproduction number Rt int…
The pandemic caused by the novel Coronavirus SARS-CoV2 has been responsible for life threatening health complications, and extreme pressure on healthcare systems. While preventive and definite curative medical interventions are yet to arrive, Non-Pharmaceutical Interventions (NPIs) like physical isolation, quarantine and drastic social measures imposed by governing agencies are effective in arresting the spread of infections in a population. In densely populated countries like India, lockdown interventions are partially effective due to social and administrative complexities. Using detailed de…
Countries around the world implement nonpharmaceutical interventions (NPIs) to mitigate the spread of COVID-19. Design of efficient NPIs requires identification of the structure of the disease transmission network. We here identify the key parameters of the COVID-19 transmission network for time periods before, during, and after the application of strict NPIs for the first wave of COVID-19 infections in Germany combining Bayesian parameter inference with an agent-based epidemiological model. We assume a Watts-Strogatz small-world network which allows to distinguish contacts within clustered cl…
When the Covid-19 pandemic enters dangerous new phase, whether and when to take aggressive public health interventions to slow down the spread of COVID-19. To develop the artificial intelligence (AI) inspired methods for real-time forecasting and evaluating intervention strategies to curb the spread of Covid-19 in the World. A modified auto-encoder for modeling the transmission dynamics of the epidemics is developed and applied to the surveillance data of cumulative and new Covid-19 cases and deaths from WHO, as of March 16, 2020. The average errors of 5-step forecasting were 2.5%. The total p…
Since the onset of the COVID-19 outbreak in Wuhan, China, numerous forecasting models have been proposed to project the trajectory of coronavirus infection cases. We propose a new discrete-time Markov chain transition matrix model that directly incorporates stochastic behavior and for which parameter estimation is straightforward from available data. Using such data from China's Hubei province (for which Wuhan is the provincial capital city), the model is shown to be flexible, robust, and accurate. As a result, it has been adopted by the first Shanghai assistance medical team in Wuhan's Jinyin…
We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the context of the COVID-19 pandemic and demonstrate the power of the simulator via several exploratory case studies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any city administration's tool kit in our march towards digital health.
At the end of 2020, policy responses to the SARS-CoV-2 outbreak have been shaken by the emergence of virus variants. The emergence of these more contagious, more severe, or even vaccine-resistant strains have challenged worldwide policy interventions. Anticipating the emergence of these mutations to plan ahead adequate policies, and understanding how human behaviors may affect the evolution of viruses by coevolution, are key challenges. In this article, we propose coevolution with genetic algorithms (GAs) as a credible approach to model this relationship, highlighting its implications, potenti…
As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on the COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well wit…
Even though laboratory and epidemiological studies have demonstrated the effects of ambient temperature on the transmission and survival of coronaviruses, not much has been done on the effects of weather on the spread of COVID-19. This study investigates the effects of temperature, humidity, precipitation, wind speed and the specific government policy intervention of partial lockdown on the new cases of COVID-19 infection in Ghana. Daily data on confirmed cases of COVID-19 from March 13, 2020 to April 21, 2020 were obtained from the official website of Our World in Data (OWID) dedicated to COV…
Given multiple new COVID-19 variants are continuously emerging, non-pharmaceutical interventions are still primary control strategies to curb the further spread of coronavirus. However, implementing strict interventions over extended periods of time is inevitably hurting the economy. With an aim to solve this multi-objective decision-making problem, we investigate the underlying associations between policies, mobility patterns, and virus transmission. We further evaluate the relative performance of existing COVID-19 control measures and explore potential optimal strategies that can strike the …
Zhang et al. (2020) used linear regression to quantify the effect of lockdowns on the number of cases of COVID-19. We show using differential equations from the susceptible-exposed-infected-recovered (SEIR) model and with an example from another location not previously considered that the Zhang et al. analysis should not be considered sound evidence that mask mandates are sufficient to control or the primary factor controlling the spread of COVID-19.
We analyze changes in the reproduction number, R, of COVID-19 in response to public health interventions. Our results indicate that public health measures undertaken in China reduced R from 1.5 in January to 0.4 in mid-March 2020. They also suggest, however, the limitations of isolation, quarantine, and large-scale attempts to limit travel. While the world-wide reproduction number briefly dropped below 1 as China implemented extensive public health measures, the introduction of the virus to other nations swiftly led to an increasing world-wide average value of R. In Italy, the nation hardest-h…
Early assessments of the spreading rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but more reliable inferences can now be made. Here, we estimate from European data that COVID-19 cases are expected to double initially every three days, until social distancing interventions slow this growth, and that the impact of such measures is typically only seen nine days - i.e. three doubling times - after their implementation. We argue that such temporal patterns are more critical than precise estimates of the basic reproduc…
During the COVID-19 pandemic, the scientific community developed predictive models to evaluate potential governmental interventions. However, the analysis of the effects these interventions had is less advanced. Here, we propose a data-driven framework to assess these effects retrospectively. We use a regularized regression to find a parsimonious model that fits the data with the least changes in the Rt parameter. Then, we postulate each jump in Rt as the effect of an intervention. Following the do-operator prescriptions, we simulate the counterfactual case by forcing Rt to stay at the pre-jum…
Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit express…
We demonstrate an approach to replicate and forecast the spread of the SARS-CoV-2 (COVID-19) pandemic using the toolkit of probabilistic programming languages (PPLs). Our goal is to study the impact of various modeling assumptions and motivate policy interventions enacted to limit the spread of infectious diseases. Using existing compartmental models we show how to use inference in PPLs to obtain posterior estimates for disease parameters. We improve popular existing models to reflect practical considerations such as the under-reporting of the true number of COVID-19 cases and motivate the nee…
We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the su…
The virus SARS-COV-2 caused disease COVID-19 has been declared a pandemic by WHO. Currently, over 210 countries and territories have been affected. Careful, well-designed drugs and vaccine for the total elimination of this virus seem to be the need of the hour. In this context, the invivo mathematical modelling studies can be extremely helpful in understanding the efficacy of the drug interventions. These studies can also help understand the role of the crucial inflammatory mediators and the behaviour of immune response towards this novel coronavirus. Motivated by these facts, in this paper, w…
We present an empirical algorithm to forecast the evolution of the number of COVID-19 symptomatic patients in the early stages of the pandemic spread and after strict social distancing interventions. The algorithm is based on a low dimensional model for the variation of the exponential growth rate that decreases after the implementation of strict social distancing measures. From the observable data given by the number of tested positive, our model estimates the number of infected hindcast introducing in the model formulation the incubation time. We also use the model to follow the number of in…
Control Intervention Strategies for Within-Host, Between-Host and their Efficacy in the Treatment, Spread of COVID-19 : A Multi Scale Modeling Approach
Objectives. Public health officials need tools to assist with anticipating the healthcare resources required to confront the SARS-COV-2 pandemic. We built a modeling tool to aid practicing public health officials with estimating healthcare demand from the pandemic in their jurisdictions and to evaluate the potential impacts of population-wide social-distancing interventions. Methods. The tool uses a SEIR compartmental model to project the local spread of the pandemic. Users input case counts, healthcare resources, and select intervention strategies to evaluate. Outputs include the number of in…
Contagious respiratory diseases, such as COVID-19, depend on sufficiently prolonged exposures for the successful transmission of the underlying pathogen. It is important for organizations to evaluate the efficacy of interventions aiming at mitigating viral transmission among their personnel. We have developed a operational risk assessment simulation framework that couples a spatial agent-based model of movement with a SIR epidemiological model to assess the relative risks of different intervention strategies. By applying our model on MIT's STATA building, we assess the impacts of three possibl…
Few African countries have reported COVID-19 case numbers above $1\,000$ as of April 18, 2020, with South Africa reporting $3\,034$ cases being hit hardest in Sub-Saharan Africa. Several African countries, especially South Africa, have already taken strong non-pharmaceutical interventions that include physical distancing, restricted economic, educational and leisure activities and reduced human mobility options. The required strengths and overall effectiveness of such interventions, however, are debated because of simultaneous but opposing interests in most African countries: strongly limited …
National responses to the Covid-19 pandemic varied markedly across countries, from business-as-usual to complete shutdowns. Policies aimed at disrupting the viral transmission cycle and preventing the healthcare system from being overwhelmed, simultaneously exact an economic toll. We developed a intervention policy model that comprised the relative human, economic and healthcare costs of non-pharmaceutical epidemic intervention and arrived at the optimal strategy using the neuroevolution algorithm. The proposed model finds the minimum required reduction in contact rates to maintain the burden …
The ongoing COVID-19 pandemic has overwhelmingly demonstrated the need to accurately evaluate the effects of implementing new or altering existing nonpharmaceutical interventions. Since these interventions applied at the societal level cannot be evaluated through traditional experimental means, public health officials and other decision makers must rely on statistical and mathematical epidemiological models. Nonpharmaceutical interventions are typically focused on contacts between members of a population, and yet most epidemiological models rely on homogeneous mixing which has repeatedly been …
We analyze an approach to managing the COVID-19 pandemic without shutting down the economy while staying within the capacity of the healthcare system. We base our analysis on a detailed heterogeneous epidemiological model, which takes into account different population groups and phases of the disease, including incubation, infection period, hospitalization, and treatment in the intensive care unit (ICU). We model the healthcare capacity as the total number of hospital and ICU beds for the whole country. We calibrate the model parameters to data reported in several recent research papers. For h…
As of November 2020, the number of COVID-19 cases is increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers ${\cal R}(t)$ for each country by integrating the equations of the classic SIR model. We cluster countries based on the estimated ${\cal R}(t)$ through a suitable time series dissimilarity. The result suggests that simple dynamical mechanisms determine how countrie…
University of Oxford（牛津大学）；University of Bristol（布里斯托大学）；Harvard University（哈佛大学）；Imperial College London（伦敦帝国学院）
To what extent are effectiveness estimates of nonpharmaceutical interventions (NPIs) against COVID-19 influenced by the assumptions our models make? To answer this question, we investigate 2 state-of-the-art NPI effectiveness models and propose 6 variants that make different structural assumptions. In particular, we investigate how well NPI effectiveness estimates generalise to unseen countries, and their sensitivity to unobserved factors. Models that account for noise in disease transmission compare favourably. We further evaluate how robust estimates are to different choices of epidemiologic…
Disease spread is a complex phenomenon requiring an interdisciplinary approach. Covid-19 exhibited a global spatial spread in a very short time frame resulting in a global pandemic. Data of web search effort in Greece on Covid-19 as a topic for one year on a weekly temporal scale were analyzed using governmental intervention measures such a s school closures, movement restrictions, national and international travelling restrictions, stay at home requirements, mask requirements, financial support measures, and epidemiological variables such as new cases and new deaths as potential explanatory c…
