scholarly journals The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0250029
Author(s):  
Michela Baccini ◽  
Giulia Cereda ◽  
Cecilia Viscardi
Keyword(s):  
Basic Reproduction Number ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Case Fatality ◽  
Parametric Bootstrap ◽  
Model Parameters ◽  
Fatality Rate ◽  
Epidemic Curve ◽  
Plausible Values ◽  
The Basic Reproduction Number

With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.

scholarly journals SEIHCRD Model for COVID-19 spread scenarios, disease predictions and estimates the basic reproduction number, case fatality rate, hospital, and ICU beds requirement

2020 ◽  
Author(s):  
Avaneesh Singh ◽  
Manish Kumar Bajpai
Keyword(s):  
Basic Reproduction Number ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Case Fatality ◽  
The United States ◽  
Fatality Rate ◽  
Hospital Beds ◽  
The Impact ◽  
Over Time ◽  
The Basic Reproduction Number

We have proposed a new mathematical method, SEIHCRD-Model that is an extension of the SEIR-Model adding hospitalized and critical twocompartments. SEIHCRD model has seven compartments: susceptible (S), exposed (E), infected (I), hospitalized (H), critical (C), recovered (R), and deceased or death (D), collectively termed SEIHCRD. We have studied COVID- 19 cases of six countries, where the impact of this disease in the highest are Brazil, India, Italy, Spain, the United Kingdom, and the United States. SEIHCRD model is estimating COVID-19 spread and forecasting under uncertainties, constrained by various observed data in the present manuscript. We have first collected the data for a specific period, then fit the model for death cases, got the values of some parameters from it, and then estimate the basic reproduction number over time, which is nearly equal to real data, infection rate, and recovery rate of COVID-19. We also compute the case fatality rate over time of COVID-19 most affected countries. SEIHCRD model computes two types of Case fatality rate one is CFR daily and the second one is total CFR. We analyze the spread and endpoint of COVID-19 based on these estimates. SEIHCRD model is time-dependent hence we estimate the date and magnitude of peaks of corresponding to the number of exposed cases, infected cases, hospitalized cases, critical cases, and the number of deceased cases of COVID-19 over time. SEIHCRD model has incorporated the social distancing parameter, different age groups analysis, number of ICU beds, number of hospital beds, and estimation of how much hospital beds and ICU beds are required in near future.

scholarly journals Estimation of the basic reproduction number, average incubation time, asymptomatic infection rate, and case fatality rate for COVID-19: Meta-analysis and sensitivity analysis

2020 ◽  
Author(s):  
Wenqing He ◽  
Grace Y. Yi ◽  
Yayuan Zhu
Keyword(s):  
Confidence Interval ◽  
Basic Reproduction Number ◽  
Incubation Time ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Meta Analysis ◽  
Case Fatality ◽  
Asymptomatic Infection ◽  
Fatality Rate ◽  
The Basic Reproduction Number

AbstractThe coronavirus disease 2019 (COVID-19) has been found to be caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). However, comprehensive knowledge of COVID-19 remains incomplete and many important features are still unknown. This manuscripts conduct a meta-analysis and a sensitivity study to answer the questions: What is the basic reproduction number? How long is the incubation time of the disease on average? What portion of infections are asymptomatic? And ultimately, what is the case fatality rate? Our studies estimate the basic reproduction number to be 3.15 with the 95% interval (2.41, 3.90), the average incubation time to be 5.08 days with the 95% confidence interval (4.77, 5.39) (in day), the asymptomatic infection rate to be 46% with the 95% confidence interval (18.48%, 73.60%), and the case fatality rate to be 2.72% with 95% confidence interval (1.29%, 4.16%) where asymptomatic infections are accounted for.

scholarly journals Mathematical Perspective of Covid-19 Pandemic: Disease Extinction Criteria in Deterministic and Stochastic Models

2020 ◽  
Author(s):  
Debadatta Adak ◽  
Abhijit Majumder ◽  
Nandadulal Bairagi
Keyword(s):  
Basic Reproduction Number ◽  
Stochastic System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Case Fatality ◽  
Deterministic System ◽  
Globally Asymptotically Stable ◽  
Epidemic Curve ◽  
Interior Equilibrium ◽  
The Basic Reproduction Number

AbstractThe world has been facing the biggest virological invasion in the form of Covid-19 pandemic since the beginning of the year 2020. In this paper, we consider a deterministic epidemic model of four compartments classified based on the health status of the populations of a given country to capture the disease progression. A stochastic extension of the deterministic model is further considered to capture the uncertainty or variation observed in the disease transmissibility. In the case of a deterministic system, the disease-free equilibrium will be globally asymptotically stable if the basic reproduction number is less than unity, otherwise, the disease persists. Using Lyapunov functional methods, we prove that the infected population of the stochastic system tends to zero exponentially almost surely if the basic reproduction number is less than unity. The stochastic system has no interior equilibrium, however, its asymptotic solution is shown to fluctuate around the endemic equilibrium of the deterministic system under some parametric restrictions, implying that the infection persists. A case study with the Covid-19 epidemic data of Spain is presented and various analytical results have been demonstrated. The epidemic curve in Spain clearly shows two waves of infection. The first wave was observed during March-April and the second wave started in the middle of July and not completed yet. A real-time basic reproduction number has been given to illustrate the epidemiological status of Spain throughout the study period. Estimated cumulative numbers of confirmed and death cases are 1,613,626 and 42,899, respectively, with case fatality rate 2.66 per cent till the deadly virus is eliminated from Spain.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals Modeling Transmission Dynamics ofStreptococcus suiswith Stage Structure and Sensitivity Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Chaojian Shen ◽  
Mingtao Li ◽  
Wei Zhang ◽  
Ying Yi ◽  
Youming Wang ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Stage Structure ◽  
Sensitivity Analyses ◽  
Effective Control ◽  
Model Parameters ◽  
Global Dynamics ◽  
Deterministic Dynamic ◽  
Globally Stable ◽  
The Basic Reproduction Number

Streptococcosis is one of the major infectious and contagious bacterial diseases for swine farm in southern China. The influence of various control measures on the outbreaks and transmission ofS. suisis not currently known. In this study, in order to explore effective control and prevention measures we studied a deterministic dynamic model with stage structure forS. suis. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows that ifℛ0<1, the disease-free equilibrium is globally stable and the disease dies out, whereas ifℛ0>1, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. The model simulations well agree with new clinical cases and the basic reproduction number of this model is about 1.1333. Some sensitivity analyses ofℛ0in terms of the model parameters are given. Our study demonstrates that combination of vaccination and disinfection of the environment are the useful control strategy forS. suis.

scholarly journals Threshold parameters for a model of epidemic spread among households and workplaces

2009 ◽  
Vol 6 (40) ◽  
pp. 979-987 ◽  
Author(s):  
L. Pellis ◽  
N. M. Ferguson ◽  
C. Fraser
Keyword(s):  
Infectious Disease ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Parameters ◽  
Epidemic Spread ◽  
Threshold Parameter ◽  
Disease Epidemiology ◽  
Infectious Disease Epidemiology ◽  
Complex Models ◽  
The Basic Reproduction Number

The basic reproduction number R 0 is one of the most important concepts in modern infectious disease epidemiology. However, for more realistic and more complex models than those assuming homogeneous mixing in the population, other threshold quantities can be defined that are sometimes more useful and easily derived in terms of model parameters. In this paper, we present a model for the spread of a permanently immunizing infection in a population socially structured into households and workplaces/schools, and we propose and discuss a new household-to-household reproduction number R H for it. We show how R H overcomes some of the limitations of a previously proposed threshold parameter, and we highlight its relationship with the effort required to control an epidemic when interventions are targeted at randomly selected households.

scholarly journals Exploring COVID-19 Daily Records of Diagnosed Cases and Fatalities Based on Simple Non-parametric Methods

2020 ◽  
Author(s):  
Hans H. Diebner ◽  
Nina Timmesfeld
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Time Lag ◽  
Case Fatality ◽  
Parametric Models ◽  
Intermediate Step ◽  
Parametric Methods ◽  
Temporal Behaviour ◽  
The Basic Reproduction Number ◽  
Non Parametric

Based on comprehensible non-parametric methods, estimates of crucial parameters that characterise the COVID-19 pandemic with a focus on the German epidemic are presented. Where appropriate, the estimates for Germany are compared with the results for six other countries (FR, IT, US, UK, ES, CH) to get an idea of the breadth of applicability and a relational understanding. Thereby, only prevalence data of daily reported new counts of diagnosed cases and fatalities provided by the ECDC are used. Where appropriate, the results are compared with conclusions drawn from using the dataset provided by the RKI. Drawing on uncertain a priori knowledge is avoided. Specifically, we present estimates for the duration from diagnosis to death being 13 days for Germany and about 2 days for Italy as the extremes. Furthermore, based on the knowledge of this time lag between diagnoses and deaths, properly delayed asymptotic as well as instantaneous fatality-case ratios are calculated having superiority compared to the commonly published case-fatality rate. The median of the time series of the instantaneous fatality-case ratio with proper delay of 13-days between cases and deaths for Germany turns out to be 0.024. Asymptotic values are presented for other countries with France ranking highest with a fatality-case ratio of almost 0.2 at its peak. The basic reproduction number, R_0, for Germany is estimated to be between 2.4 and 3.4. The uncertainty stems from uncertain knowledge of the generation time. A delay autocorrelation shows resonances at about 4 days and 7 days, where the latter resonance is at least partially attributable to the sampling process with weekly periodicity. The calculation of the basic reproduction number is based on an evaluation of cumulative numbers of cases yielding time-dependent doubling times as an intermediate step. This allows to infer to the reproduction number during the early phase of onset of the epidemic. In a second approach, the instantaneous basic reproduction number is derived from the incident (counts of new) cases and allows, in contrast to the first version, to infer to the temporal behaviour of the reproduction number during the later epidemic course. To conclude, by avoiding complicated parametric models we provide insights into basic features of the COVID-19 epidemic in an utmost transparent and comprehensible way.

scholarly journals SEAMHCRD deterministic compartmental model based on clinical stages of infection for COVID-19 pandemic in Sultanate of Oman

2020 ◽  
Author(s):  
Abraham Varghese ◽  
Shajidmon Kolamban ◽  
Vinu Sherimon ◽  
Eduardo M. Lacap ◽  
Saad Salman Ahmed ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Research Work ◽  
Contact Tracing ◽  
Model Parameters ◽  
Policy Makers ◽  
Estimated Parameters ◽  
Short Period ◽  
Reported Data

Abstract The present novel corona virus (COVID-19) infection has engendered a worldwide crisis across the world in an enormous scale within a very short period. The effective solution for this pandemic is to recognize the nature and spread of the disease so that appropriate policies can be framed. Mathematical modelling is always at the forefront to understand and provide an adequate description about the transmission of any disease. In this research work, we have formulated a deterministic compartmental model (SEAMHCRD) including various stages of infection, such as Mild, Moderate, Severe and Critical to study the spreading of COVID-19 and estimated the model parameters by fitting the model with the reported data of ongoing pandemic in Oman. The steady state, stability and final pandemic size of the model has been proved mathematically. The various transmission as well as transition parameters are estimated during the period from June 8th - July 30th, 2020. Based on the current estimated parameters, the pandemic size is also predicted for another 100 days. Sensitivity analysis is performed to identify the key model parameters, and corresponding basic reproduction number has been computed using Next Generation Matrix (NGM) method. As the value of basic reproduction number (R0) is 0.9761 during the period from June 8th - July 30th, 2020, it is an indication for the policy makers to adopt appropriate remedial measures like social distancing and contact tracing to reduce the value of R0 to control the spread of the disease.

Sign in / Sign up

Export Citation Format

Share Document