scholarly journals Covid-19 disease dynamics with vaccination: The effect of uncertainty

2022 ◽  
Author(s):  
Nandadulal Bairagi ◽  
Abhijiit Majumder
Keyword(s):  
Mathematical Models ◽  
Vaccine Efficacy ◽  
Loss Rate ◽  
Vaccination Rate ◽  
Model Parameters ◽  
Extinction Time ◽  
Disease Eradication ◽  
Average Value ◽  
Force Of Infection ◽  
Induced Immunity

Rate parameters are critical in estimating the covid burden using mathematical models. In the Covid-19 mathematical models, these parameters are assumed to be constant. However, uncertainties in these rate parameters are almost inevitable. In this paper, we study a stochastic epidemic model of the SARS-CoV-2 virus infection in the presence of vaccination in which some parameters fluctuate around its average value. Our analysis shows that if the stochastic basic reproduction number (SBRN) of the system is greater than unity, then there is a stationary distribution, implying the long-time disease persistence. A sufficient condition for disease eradication is also prescribed for which the exposed class goes extinct, followed by the infected class. The disease eradication criterion may not hold if the rate of vaccine-induced immunity loss increases or/and the force of infection increases. Using the Indian Covid-19 data, we estimated the model parameters and showed the future disease progression in the presence of vaccination. The disease extinction time is estimated under various conditions. It is revealed that the mean extinction time is an increasing function of both the force of infection and immunity loss rate and shows the lognormal distribution. We point out that disease eradication might not be possible even at a higher vaccination rate if the vaccine-induced immunity loss rate is high. Our observation thus indicates the endemicity of the disease for the existing vaccine efficacy. The disease eradication is possible only with a higher vaccine efficacy or a reduced infection rate.

Pertussis in England and Wales: an investigation of transmission dynamics and control by mass vaccination

1989 ◽  
Vol 236 (1284) ◽  
pp. 213-252 ◽  
Keyword(s):  
Mathematical Models ◽  
Vaccine Efficacy ◽  
Case Reports ◽  
Mass Vaccination ◽  
Vaccine Uptake ◽  
Transmission Dynamics ◽  
England And Wales ◽  
Epidemic Period ◽  
The Impact ◽  
Induced Immunity

The epidemiology of pertussis and its prospects for control by mass vaccination in England and Wales are investigated by analyses of longitudinal records on incidence and vaccine uptake, and horizontal data on age-stratified case reports. Mathematical models of the transmission dynamics of the infection that incorporate loss of natural and vaccine-induced immunity plus variable vaccine efficacy are developed, and their predictions compared with observed trends. Analyses of case reports reveal that the individual force of infection is age dependent, with peak transmission in the 5- to 10-year-old age class. A model incorporating this age dependency, along with partial vaccine efficacy and loss of vaccine-induced immunity, generates predicted patterns that best mirror observed trends since mass vaccination was inaugurated in 1957 in England and Wales. Model projections accurately mirror the failure of mass vaccination to increase the inter-epidemic period of the infection (three years) over that pertaining before control. The analysis suggests that this is due to the impact of partial vaccine efficacy. Projected trends to not accurately reflect the low levels of pertussis incidence reported between epidemics in the periods of high vaccine uptake. This is thought to arise from a combination of factors, including loss of natural and vaccine induced immunity, biases in case reporting (where reporting efficiency is positively associated with the incidence of pertussis), and seasonal variations in transmission. Model predictions suggest that the vaccination of 88% of each birth cohort before the age of 1 year will eliminate bacterial transmission, provided the vaccine confers lifelong protection against infection. If vaccine-induced immunity is significantly less than lifelong (or if vaccination fails to protect all its recipients) repeated cohort immunization is predicted to be necessary to eliminate transmission. Future research needs are discussed, and emphasis is placed on the need for more refined data on vaccine efficacy, the duration of natural and vaccine-induced immunity and the incidence of clinical pertussis and subclinical infections (perhaps by the development of reliable serological tests). Future mathematical models will need especially to incorporate seasonality in transmission.

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 Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential

Cells ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 1516
Author(s):  
Daniel Gratz ◽  
Alexander J Winkle ◽  
Seth H Weinberg ◽  
Thomas J Hund
Keyword(s):  
Action Potential ◽  
Mathematical Models ◽  
Cardiac Myocyte ◽  
Population Level ◽  
Na Channel ◽  
Model Parameters ◽  
Healthy Population ◽  
Experimental Measurements ◽  
Voltage Gated ◽  
Experimental Variability

The voltage-gated Na+ channel Nav1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Nav1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Nav1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Nav1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

scholarly journals Host Factors Impact Vaccine Efficacy: Implications for Seasonal and Universal Influenza Vaccine Programs

2019 ◽  
Vol 93 (21) ◽  
Author(s):  
Santosh Dhakal ◽  
Sabra L. Klein
Keyword(s):  
Influenza Virus ◽  
Influenza Vaccine ◽  
Virus Vaccine ◽  
Vaccine Efficacy ◽  
Public Health Problem ◽  
Influenza Virus Vaccine ◽  
Host Factors ◽  
Influenza Vaccines ◽  
Vaccine Type ◽  
Induced Immunity

ABSTRACT Influenza is a global public health problem. Current seasonal influenza vaccines have highly variable efficacy, and thus attempts to develop broadly protective universal influenza vaccines with durable protection are under way. While much attention is given to the virus-related factors contributing to inconsistent vaccine responses, host-associated factors are often neglected. Growing evidences suggest that host factors including age, biological sex, pregnancy, and immune history play important roles as modifiers of influenza virus vaccine efficacy. We hypothesize that host genetics, the hormonal milieu, and gut microbiota contribute to host-related differences in influenza virus vaccine efficacy. This review highlights the current insights and future perspectives into host-specific factors that impact influenza vaccine-induced immunity and protection. Consideration of the host factors that affect influenza vaccine-induced immunity might improve influenza vaccines by providing empirical evidence for optimizing or even personalizing vaccine type, dose, and use of adjuvants for current seasonal and future universal influenza vaccines.

scholarly journals Simple mathematical models for controlling COVID-19 transmission through social distancing and community awareness

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahmed S. Elgazzar
Keyword(s):  
Mathematical Models ◽  
Virus Transmission ◽  
Small World ◽  
Vaccination Rate ◽  
The Novel ◽  
Social Distancing ◽  
Community Awareness ◽  
Sufficient Degree ◽  
And Control

Abstract The novel COVID-19 pandemic is a current, major global health threat. Up till now, there is no fully approved pharmacological treatment or a vaccine. Also, its origin is still mysterious. In this study, simple mathematical models were employed to examine the dynamics of transmission and control of COVID-19 taking into consideration social distancing and community awareness. Both situations of homogeneous and nonhomogeneous population were considered. Based on the calculations, a sufficient degree of social distancing based on its reproductive ratio is found to be effective in controlling COVID-19, even in the absence of a vaccine. With a vaccine, social distancing minimizes the sufficient vaccination rate to control the disease. Community awareness also has a great impact in eradicating the virus transmission. The model is simulated on small-world networks and the role of social distancing in controlling the infection is explained.

scholarly journals Integrating multimodal data sets into a mathematical framework to describe and predict therapeutic resistance in cancer

2020 ◽  
Author(s):  
Kaitlyn Johnson ◽  
Grant R. Howard ◽  
Daylin Morgan ◽  
Eric A. Brenner ◽  
Andrea L. Gardner ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Single Cell ◽  
Treatment Response ◽  
Model Parameters ◽  
Data Sets ◽  
Response Dynamics ◽  
Multimodal Data ◽  
Transcriptomic Data ◽  
Treatment Regimens ◽  
New Treatment

SummaryA significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other data types. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic mechanistic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal population-size data. We demonstrate that the explicit inclusion of the transcriptomic information in the parameter estimation is critical for identification of the model parameters and enables accurate prediction of new treatment regimens. Inclusion of the transcriptomic data improves predictive accuracy in new treatment response dynamics with a concordance correlation coefficient (CCC) of 0.89 compared to a prediction accuracy of CCC = 0.79 without integration of the single cell RNA sequencing (scRNA-seq) data directly into the model calibration. To the best our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with longitudinal treatment response data into a mechanistic mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multimodal data sets into identifiable mathematical models to develop optimized treatment regimens from data.

scholarly journals Will the Large-scale Vaccination Succeed in Containing the COVID-19 Epidemic and How Soon?

2021 ◽  
Author(s):  
Shilei Zhao ◽  
Tong Sha ◽  
Yongbiao Xue ◽  
Chung-I Wu ◽  
Hua Chen
Keyword(s):  
United States Of America ◽  
Vaccine Efficacy ◽  
Large Scale ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Epidemic Dynamics ◽  
Intervention Measures ◽  
Vaccination Scheme ◽  
Mutant Strains ◽  
Promising Solution

The availability of vaccines provides a promising solution to containing the COVID-19 pandemic. Here, we develop an epidemiological model to quantitatively analyze and predict the epidemic dynamics of COVID-19 under vaccination. The model is applied to the daily released numbers of confirmed cases of Israel and United States of America to explore and predict the trend under vaccination based on their current epidemic status and intervention measures. For Israel, of which 53.83% of the population was fully vaccinated, under the current intensity of NPIs and vaccination scheme, the pandemic is predicted to end between May 14, 2021 to May 16, 2021 depending on an immunity duration between 180 days and 365 days; Assuming no NPIs after March 24, 2021, the pandemic will ends later, between July 4, 2021 to August 26, 2021. For USA, if we assume the current vaccination rate (0.268% per day) and intensity of NPIs, the pandemic will end between February 3, 2022 and August 17, 2029 depending on an immunity duration between 180 days and 365 days. However, assuming an immunity duration of 180 days and with no NPIs, the pandemic will not end, and instead reach an equilibrium state with a proportion of the population remaining actively infected. Overall the daily vaccination rate should be chosen according to the vaccine efficacy and the immunity duration to achieve herd immunity. In some situations, vaccination alone cannot stop the pandemic, and NPIs are necessary both to supplement vaccination and accelerate the end of the pandemic. Considering that vaccine efficacy and duration of immunity may be reduced for new mutant strains, it is necessary to remain cautiously optimistic about the prospect of the pandemic under vaccination.

scholarly journals SARS-CoV-2 Convalescent Sera Binding and Neutralizing Antibody Concentrations Compared with COVID-19 Vaccine Efficacy Estimates Against Symptomatic Infection

2021 ◽  
Author(s):  
Amy J. Schuh ◽  
Panayampalli S. Satheshkumar ◽  
Stephanie Dietz ◽  
Lara Bull-Otterson ◽  
Myrna Charles ◽  
...  
Keyword(s):  
Vaccine Efficacy ◽  
Neutralizing Antibody ◽  
Published Data ◽  
Symptomatic Infection ◽  
Convenience Sample ◽  
Post Vaccination ◽  
Antibody Assays ◽  
Study Population ◽  
Binding Antibody ◽  
Induced Immunity

Previous vaccine efficacy (VE) studies have estimated neutralizing and binding antibody concentrations that correlate with protection from symptomatic infection; how these estimates compare to those generated in response to SARS-CoV-2 infection is unclear. Here, we assessed quantitative neutralizing and binding antibody concentrations using standardized SARS-CoV-2 assays on 3,067 serum specimens collected during July 27, 2020-August 27, 2020 from COVID-19 unvaccinated persons with detectable anti-SARS-CoV-2 antibodies using qualitative antibody assays. Quantitative neutralizing and binding antibody concentrations were strongly positively correlated (r=0.76, p<0.0001) and were noted to be several fold lower in the unvaccinated study population as compared to published data on concentrations noted 28 days post-vaccination. In this convenience sample, ~88% of neutralizing and ~63-86% of binding antibody concentrations met or exceeded concentrations associated with 70% COVID-19 VE against symptomatic infection from published VE studies; ~30% of neutralizing and 1-14% of binding antibody concentrations met or exceeded concentrations associated with 90% COVID-19 VE. These data support observations of infection-induced immunity and current recommendations for vaccination post infection to maximize protection against symptomatic COVID-19.

scholarly journals The Influence of Water on the Heat Loss of Hot Mix Asphalt

2019 ◽  
Vol 9 (9) ◽  
pp. 1747
Author(s):  
Paweł Mieczkowski ◽  
Bartosz Budziński
Keyword(s):  
Hot Mix Asphalt ◽  
Specific Property ◽  
External Factors ◽  
Model Parameters ◽  
Thermal Processes ◽  
Average Value ◽  
Influence Of Water ◽  
Boiling And Evaporation ◽  
The Heat Transfer Coefficient ◽  
Specimen Section

Compaction of hot mix asphalt (HMA) is a process of altering the internal structure of the material and, as a consequence, also its performance characteristics. The process should ensure the adequate viscosity of binder, a property depending on the temperature and the material-specific property (hardness) of the binder (in the case of HMA). One of the external factors that can affect the process of compaction is the presence of water quickly decreasing the HMA temperature. This paper presents a theoretical model for determining the HMA temperature variation under the effect of water. One of the model parameters is the heat transfer coefficient α for the outward flow of heat. Its value varies strongly in the interfacial zones of the HMA layer (i.e., near the top and bottom surfaces) due to the effect of external factors. The paper presents the attempt to estimate the average value for the whole paving process depending on the precipitation rate (amount of water involved in the process). The temperatures obtained from the model were verified experimentally on laboratory specimens cooled with water. The temperature was measured on the surface and across the specimen section. The drop of temperature of HMA was almost instantaneous on the surface—due to the thermal processes involving water (boiling and evaporation)—and much slower across the layer thickness.

scholarly journals SARS-CoV-2 Omicron Spike recognition by plasma from individuals receiving BNT162b2 mRNA vaccination with a 16-weeks interval between doses

2021 ◽  
Author(s):  
Debashree Chatterjee ◽  
Alexandra Tauzin ◽  
Lorie Marchitto ◽  
Shang Yu Gong ◽  
Marianne Boutin ◽  
...  
Keyword(s):  
Clinical Benefit ◽  
Vaccine Efficacy ◽  
Short Interval ◽  
Antigenic Drift ◽  
Alpha Beta ◽  
Induced Immunity ◽  
Plasma Activity

Continuous emergence of SARS-CoV-2 variants of concern (VOC) is fueling the COVID-19 pandemic. Omicron (B.1.1.529), is rapidly spreading worldwide. The large number of mutations in its Spike raised concerns about a major antigenic drift that could significantly decrease vaccine efficacy and infection-induced immunity. A long interval between BNT162b2 mRNA doses was shown to elicit antibodies that efficiently recognize Spikes from different VOCs. Here we evaluated the recognition of Omicron Spike by plasma from a cohort of SARS-CoV-2 naive and previously-infected individuals that received their BNT162b2 mRNA vaccine 16-weeks apart. Omicron Spike was recognized less efficiently than D614G, Alpha, Beta, Gamma and Delta Spikes. We compared to plasma activity from participants receiving a short (4-weeks) interval regimen. Plasma from individuals of the long interval cohort neutralized better the Omicron Spike compared to those that received a short interval. Whether this difference confers any clinical benefit against Omicron remains unknown.

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