scholarly journals Modeling The Impact of Vaccination On COVID-19 And Its Delta Variant

2021 ◽  
Author(s):  
Jianbo Wang ◽  
Yin-Chi Chan ◽  
Ruiwu Niu ◽  
Eric W. M. Wong ◽  
Michaël Antonie Van Wyk
Keyword(s):  
Hong Kong ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Hospitalization Rate ◽  
Model Parameters ◽  
Cumulative Number ◽  
Reproduction Numbers ◽  
Important Means ◽  
Model Initialization ◽  
The Impact

Abstract Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example to prove the validity of our model. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced had vaccination been available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral and Delta strains of the virus. Next, we compare the evolution of the SVEIHR model to the traditional “herd immunity” threshold where the proportion of vaccinated individuals is static and no further vaccination takes place after model initialization. Numerical results for Hong Kong demonstrate that the static herd immunity threshold corresponds to a cumulative hospitalization ratio of about one percent (assuming the current hospitalization rate of infected individuals is maintained). We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered for while still maintaining the same proportion of cumulative hospitalized individuals.

scholarly journals The Effect of Vaccination Rates on the Infection of COVID-19 under the Vaccination Rate below the Herd Immunity Threshold

2021 ◽  
Vol 18 (14) ◽  
pp. 7491
Author(s):  
Yi-Tui Chen
Keyword(s):  
Infection Rate ◽  
Herd Immunity ◽  
The United States ◽  
Vaccination Rate ◽  
Infection Rates ◽  
Vaccination Rates ◽  
The United Kingdom ◽  
The World ◽  
Almost All ◽  
The Impact

Although vaccination is carried out worldwide, the vaccination rate varies greatly. As of 24 May 2021, in some countries, the proportion of the population fully vaccinated against COVID-19 has exceeded 50%, but in many countries, this proportion is still very low, less than 1%. This article aims to explore the impact of vaccination on the spread of the COVID-19 pandemic. As the herd immunity of almost all countries in the world has not been reached, several countries were selected as sample cases by employing the following criteria: more than 60 vaccine doses per 100 people and a population of more than one million people. In the end, a total of eight countries/regions were selected, including Israel, the UAE, Chile, the United Kingdom, the United States, Hungary, and Qatar. The results find that vaccination has a major impact on reducing infection rates in all countries. However, the infection rate after vaccination showed two trends. One is an inverted U-shaped trend, and the other is an L-shaped trend. For those countries with an inverted U-shaped trend, the infection rate begins to decline when the vaccination rate reaches 1.46–50.91 doses per 100 people.

scholarly journals Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Randy L. Caga-anan ◽  
Michelle N. Raza ◽  
Grace Shelda G. Labrador ◽  
Ephrime B. Metillo ◽  
Pierre del Castillo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Disease Progression ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
The Philippines ◽  
Model Parameters ◽  
Delay Term ◽  
Induced Immunity ◽  
Determining Factor ◽  
Disease Free

Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

scholarly journals Mathematical Analysis of Malaria-Schistosomiasis Coinfection Model

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
E. A. Bakare ◽  
C. R. Nwozo
Keyword(s):  
Numerical Simulations ◽  
Endemic Equilibrium ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Reproduction Numbers ◽  
Mathematical Techniques ◽  
Parameter Values ◽  
The Impact ◽  
Number Of Individuals ◽  
Disease Free

We formulated and analysed a mathematical model to explore the cointeraction between malaria and schistosomiasis. Qualitative and comprehensive mathematical techniques have been applied to analyse the model. The local stability of the disease-free and endemic equilibrium was analysed, respectively. However, the main theorem shows that if RMS<1, then the disease-free equilibrium is locally asymptotically stable and the phase will vanish out of the host and if RMS>1, a unique endemic equilibrium is also locally asymptotically stable and the disease persists at the endemic steady state. The impact of schistosomiasis and its treatment on malaria dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics coexist whenever their reproduction numbers exceed unity. Further, results of the full malaria-schistosomiasis model also suggest that an increase in the number of individuals infected with schistosomiasis in the presence of treatment results in a decrease in malaria cases. Sensitivity analysis was further carried out to investigate the influence of the model parameters on the transmission and spread of malaria-schistosomiasis coinfection. Numerical simulations were carried out to confirm our theoretical findings.

scholarly journals Interpreting airborne pandemics spreading using fractal kinetics’ principles

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 609
Author(s):  
Panos Macheras ◽  
Athanasios A. Tsekouras ◽  
Pavlos Chryssafidis
Keyword(s):  
Preventive Measures ◽  
Herd Immunity ◽  
Real Life ◽  
Kinetics Model ◽  
Mixed System ◽  
Model Parameters ◽  
Population Mobility ◽  
Fractal Kinetics ◽  
Time Model ◽  
The Impact

Introduction  The reaction between susceptible and infected subjects has been studied under the well-mixed hypothesis for almost a century. Here, we present a consistent analysis for a not well-mixed system using fractal kinetics’ principles.  Methods  We analyzed COVID-19 data to get insights on the disease spreading in absence/presence of preventive measures. We derived a three-parameter model and show that the “fractal” exponent h of time larger than unity can capture the impact of preventive measures affecting population mobility.  Results  The h=1 case, which is a power of time model, accurately describes the situation without such measures in line with a herd immunity policy. The pandemic spread in four model countries (France, Greece, Italy and Spain) for the first 10 months has gone through four stages: stages 1 and 3 with limited to no measures, stages 2 and 4 with varying lockdown conditions. For each stage and country two or three model parameters have been determined using appropriate fitting procedures. The fractal kinetics model was found to be more akin to real life.  Conclusion  Model predictions and their implications lead to the conclusion that the fractal kinetics model can be used as a prototype for the analysis of all contagious airborne pandemics.

scholarly journals Impact of booster COVID-19 vaccine for Moroccan adults: A discrete age-structured model approach

2021 ◽  
Author(s):  
Aayah Hammoumi ◽  
Hanane Hmarrass ◽  
Redouane Qesmi
Keyword(s):  
Vaccine Efficacy ◽  
Adult Population ◽  
Herd Immunity ◽  
Vaccine Uptake ◽  
Vaccination Program ◽  
Model Parameters ◽  
Structured Model ◽  
Age Structured ◽  
Age Structured Model ◽  
The Impact

AbstractPublic health control strategies, such as lockdown, seem to be effective in reducing the spread of the pandemic, but are ineffective as a whole since lockdown is responsible of global economic crisis and badly lived by the majority of children and adults who have developed mental health disorders and familial problems as well. Thus, the development of a vaccine against COVID-19 is needed to control this disease. We have developed a discrete age-structured model and followed the Moroccan vaccination program to assess the impact of booster vaccination targeting Moroccan adults against COVID-19. Using the derived model, we estimated some relevant model parameters related to COVID-19 using collected cumulative mortality and reported Moroccan data. A control reproduction number Rc, which determines the necessary level of vaccine uptake that lead to COVID-19 eradication is determined. Furthermore, a herd immunity threshold above which the population can be protected from COVID-19 infection is derived. Analyzing the model, sufficient and necessary conditions for the eradication of the disease are obtained as well. Next, we perform numerical simulations to study the impact of several uptake levels of the potential vaccine on the persistence and the extinction of COVID-19 pandemic. Our results show that the COVID-19 is expected to last past 2021 in the absence of a vaccination program. Moreover, a vaccination of the adult population at rate 0.6% per day needs at least 67% of vaccine efficacy and 90% of immunogenicity rate to eradicate the disease. Using Sinopharm vaccine, the herd immunity can be achieved when about half of Moroccan adult population is immunized against the COVID-19. However, using Oxford-Astrazeneca vaccine, less than 60% of adult population must be immunized against the disease to achieve the herd immunity. Finally, if vaccine efficacy is about 80% and the immunogenicity is about 50% then vaccinating adults at rate of 0.6% per day could protect roughly 22% of children from COVID-19 infection.

scholarly journals Monitoring and forecasting the SARS-Covid-19 pandemic in France

2021 ◽  
Author(s):  
Juergen Reingruber ◽  
Andrea Papale ◽  
Stephane Ruckly ◽  
Jean-Francois Timsit ◽  
David Holcman
Keyword(s):  
Social Dynamics ◽  
National Level ◽  
Herd Immunity ◽  
Model Parameters ◽  
Modelling Framework ◽  
Infection Dynamics ◽  
Reproduction Numbers ◽  
Monitoring And Forecasting ◽  
Inference Methods ◽  
Near Future

Over the past year, many countries have resorted multiple times to drastic social restrictions to prevent saturation of their health care system, and to regain control over an otherwise exponentially increasing SARS-Covid-19 pandemic evolution. With the advent of data-sharing, computational approaches have gained a key role in evaluating future scenarios and offering predictions in a constantly evolving social environment. To design optimal social, hospitalization and economical strategies that guarantee control over the pandemic progression, we developed a data-driven modelling framework with the aim to provide reliable near future predictions under constantly evolving social and pandemic events. The framework is flexible enough to be used at a single hospital, regional or national level. We used a variety of data such as social, serological, testing and clinical data to compute the infection dynamics and the hospital workload for France. We developed inference methods to calibrate model parameters from observed hospitalization statistics over adjustable time periods. We applied our model to study the age stratified pandemic evolution inside and outside hospitals until February 2021, and the competition between vaccinations and the novel delta variant. We obtained several predictions about hidden pandemic properties such as fractions of infected, infection hospitality and infection fatality ratios. We show that reproduction numbers and herd immunity levels are not universal but strongly depend on the underlying social dynamics. We find that with normal social interactions the present vaccination status and rate is not sufficient to prevent a new pandemic wave driven by the delta variant.

scholarly journals initMIP-Antarctica: An ice sheet model initialization experiment of ISMIP6

2019 ◽  
Author(s):  
Hélène Seroussi ◽  
Sophie Nowicki ◽  
Erika Simon ◽  
Ayako Abe Ouchi ◽  
Torsten Albrecht ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Ice Sheet ◽  
Model Parameters ◽  
Model Intercomparison ◽  
Ice Shelves ◽  
External Forcings ◽  
Intercomparison Project ◽  
Model Initialization ◽  
Basal Melting ◽  
The Impact

Abstract. Ice sheet numerical modeling is the best approach to estimate the dynamic contribution of Antarctica to sea level rise over the coming centuries. The influence of initial conditions on ice sheet model simulations, however, is still unclear. To better understand this influence, an initial state intercomparison exercise (initMIP) has been developed to compare, evaluate, and improve initialization procedures and estimate their impact on century-scale simulations. initMIP is the first set of experiments of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity focusing on the Greenland and Antarctic Ice Sheets. Following initMIP-Greenland, initMIP-Antarctica has been designed to explore uncertainties associated with model initialization and spin-up and to evaluate the impact of changes in external forcings. Starting from the state of the Antarctic ice sheet at the end of the initialization procedure, three forward experiments are each run for 100 years: a control run, a run with a surface mass balance (SMB) anomaly, and a run with a basal melting anomaly beneath floating ice. This study presents the results of initMIP-Antarctica from 25 simulations performed by 16 international modeling groups. The submitted results use different initial conditions and initialization methods, as well as ice flow model parameters and reference external forcings. We find a good agreement among model responses to the SMB anomaly, but large variations in responses to the basal melting anomaly. These variations can be attributed to differences in the extent of ice shelves and their upstream tributaries, the numerical treatment of grounding line, as well as the initial ocean conditions applied, suggesting that ongoing efforts to better represent ice shelves in continental-scale models should continue.

scholarly journals Modelling Seasonal Brucellosis Epidemics in Bayingolin Mongol Autonomous Prefecture of Xinjiang, China, 2010–2014

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Pengwei Lou ◽  
Lei Wang ◽  
Xueliang Zhang ◽  
Jiabo Xu ◽  
Kai Wang
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Rate ◽  
Human Brucellosis ◽  
Model Parameters ◽  
Cumulative Number ◽  
Effective Strategies ◽  
Reported Data ◽  
Periodic Transmission ◽  
The Basic Reproduction Number

Brucellosis is one of the severe public health problems; the cumulative number of new human brucellosis cases reached 211515 from 2010 to 2014 in China. Bayingolin Mongol Autonomous Prefecture is situated in the southeast of Xinjiang, where brucellosis infection occurs every year. Based on the reported data of newly acute human brucellosis cases for each season in Bayingolin Mongol Autonomous Prefecture, we proposed a susceptible, exposed, infected, and vaccinated (SEIV) model with periodic transmission rates to investigate the seasonal brucellosis transmission dynamics among sheep/cattle and from sheep/cattle to humans. Compared with the criteria of MAPE and RMSPE, the model simulations agree to the data on newly acute human brucellosis. We predict that the number of newly acute human brucellosis is increasing and will peak 15325 [95% CI: 11920–18242] around the summer of 2023. We also estimate the basic reproduction numberR0=2.5524[95% CI: 2.5129–2.6225] and perform some sensitivity analysis of the newly acute human brucellosis cases and the basic reproduction numberR0in terms of model parameters. Our study demonstrates that reducing the birth number of sheep/cattle, raising the slaughter rate of infected sheep/cattle, increasing the vaccination rate of susceptible sheep/cattle, and decreasing the loss rate of vaccination are effective strategies to control brucellosis epidemic.

scholarly journals High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200354 ◽  
Author(s):  
Carmen B. Acosta-Alonzo ◽  
Igor V. Erovenko ◽  
Aaleah Lancaster ◽  
Hyunju Oh ◽  
Jan Rychtář ◽  
...  
Keyword(s):  
Typhoid Fever ◽  
Rural Areas ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Epidemiological Model ◽  
Model Parameters ◽  
Theoretic Model ◽  
Vaccination Rates ◽  
Incidence Data ◽  
Optimal Population

Typhoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a game-theoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic life-long carriers but also for a short-cycle transmission in the immediate environment and a long-cycle transmission via contamination of the water supply. We calibrated the model parameters based on the known incidence data. We found that unless the (perceived) cost of vaccination is negligible, the individually optimal population vaccination rate falls significantly short of the societally optimal population vaccination rate needed to reach herd immunity. We expressed both the herd immunity and the optimal equilibrium vaccination rates in terms of only a few observable parameters such as the incidence rate, demographics, vaccine waning rate and the perceived cost of vaccination relative to the cost of infection. This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.

scholarly journals Estimating the herd immunity threshold by accounting for the hidden asymptomatics using a COVID-19 specific model

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242132
Author(s):  
Shaurya Kaushal ◽  
Abhineet Singh Rajput ◽  
Soumyadeep Bhattacharya ◽  
M. Vidyasagar ◽  
Aloke Kumar ◽  
...  
Keyword(s):  
Real World ◽  
Analytic Solution ◽  
Herd Immunity ◽  
Epidemiological Data ◽  
Specific Model ◽  
Model Parameters ◽  
Parametric Form ◽  
Real World Data ◽  
Asymptomatic Patients ◽  
The Impact

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lock-down and resulting spatial migration of population due to announcement of lock-down. A method is presented for estimating the model parameters from real-world data, and it is shown that the various phases in the observed epidemiological data are captured well. It is shown that increase of infections slows down and herd immunity is achieved when active symptomatic patients are 10-25% of the population for the four countries we studied. Finally, a method for estimating the number of asymptomatic patients, who have been the key hidden link in the spread of the infections, is presented.

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