scholarly journals Estimation of the basic reproduction number of measles during an outbreak in a partially vaccinated population

2000 ◽  
Vol 124 (2) ◽  
pp. 273-278 ◽  
Author(s):  
J. MOSSONG ◽  
C. P. MULLER
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Primary Schools ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
School Settings ◽  
Measles Outbreak ◽  
Major Outbreak ◽  
School Surveys ◽  
The Basic Reproduction Number

From March to July 1996 a measles outbreak occurred in northern Luxembourg with 110 reported cases centered around two primary schools (85 cases) and the surrounding community (25 cases). Eighty four suspected cases were confirmed serologically. Vaccine coverage was estimated from questionnaire-based surveys at the two primary schools to be 70 and 76%, respectively. Vaccine efficacy during the outbreak was estimated to be 94.6% [95% confidence interval (CI) 90·4–97·0]. Using the information from the school surveys, we obtained estimates of the basic reproduction number of measles of 7·7 (95% CI 4·4–11·0) and 6·2 (95% CI 3·5–8·9), respectively. Assuming a 95% vaccine efficacy, these estimates correspond to minimal vaccine coverages of 91·6% (95% CI 81·4–95·7) and 88·3% (95% CI 75·5–93·4) which would have been necessary to minimize the chances of a major outbreak occurring. We can confirm that major outbreaks in similar school settings can only be prevented if vaccination coverage exceeds 90%.

scholarly journals A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

2021 ◽  
Author(s):  
John S Dagpunar ◽  
ChenChen Wu
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Infection Prevalence ◽  
State Variables ◽  
Susceptible Population ◽  
Waning Immunity ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, for an infectious disease such as Covid-19, we present a SIR model which examines the impact of waning immunity, vaccination rates, vaccine efficacy, and the proportion of the susceptible population who aspire to be vaccinated. Under an assumed constant control reproduction number, we provide simple conditions for the disease to be eliminated, and conversely for it to exhibit the more likely endemic behaviour. With regard to Covid-19, it is shown that if the control reproduction number is set to the basic reproduction number (say 6) of the dominant delta (B1.617.2) variant, vaccination alone, even under the most optimistic of assumptions about vaccine efficacy and high vaccine coverage, is very unlikely to lead to elimination of the disease. The model is not intended to be predictive but more an aid to understanding the relative importance of various biological and control parameters. For example, from a long-term perspective, it may be found that in the UK, through changes in societal behaviour (such as mask use, ventilation, and level of homeworking), without formal government interventions such as on-off lockdowns, the control reproduction number can still be maintained at a level significantly below the basic reproduction number. Even so, our simulations show that endemic behaviour ensues. The model obtains equilibrium values of the state variables such as the infection prevalence and mortality rate under various scenarios.

scholarly journals Graphs with specified degree distributions, simple epidemics, and local vaccination strategies

2007 ◽  
Vol 39 (04) ◽  
pp. 922-948 ◽  
Author(s):  
Tom Britton ◽  
Svante Janson ◽  
Anders Martin-Löf
Keyword(s):  
Infectious Disease ◽  
Social Structure ◽  
Basic Reproduction Number ◽  
Degree Distribution ◽  
Reproduction Number ◽  
Final Size ◽  
Vaccination Strategies ◽  
The Social ◽  
Major Outbreak ◽  
The Basic Reproduction Number

Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R 0, the basic reproduction number, and τ0, the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine R v , the reproduction number, and τ v , the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.

scholarly journals Effect of evidence updates on key determinants of measles vaccination impact: a DynaMICE modelling study in ten high-burden countries

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Han Fu ◽  
Kaja Abbas ◽  
Petra Klepac ◽  
Kevin van Zandvoort ◽  
Hira Tanvir ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Case Fatality ◽  
Routine Immunisation ◽  
High Burden ◽  
Fatality Risk ◽  
Measles Vaccination ◽  
Case Fatality Risk ◽  
The Basic Reproduction Number

Abstract Background Model-based estimates of measles burden and the impact of measles-containing vaccine (MCV) are crucial for global health priority setting. Recently, evidence from systematic reviews and database analyses have improved our understanding of key determinants of MCV impact. We explore how representations of these determinants affect model-based estimation of vaccination impact in ten countries with the highest measles burden. Methods Using Dynamic Measles Immunisation Calculation Engine (DynaMICE), we modelled the effect of evidence updates for five determinants of MCV impact: case-fatality risk, contact patterns, age-dependent vaccine efficacy, the delivery of supplementary immunisation activities (SIAs) to zero-dose children, and the basic reproduction number. We assessed the incremental vaccination impact of the first (MCV1) and second (MCV2) doses of routine immunisation and SIAs, using metrics of total vaccine-averted cases, deaths, and disability-adjusted life years (DALYs) over 2000–2050. We also conducted a scenario capturing the effect of COVID-19 related disruptions on measles burden and vaccination impact. Results Incorporated with the updated data sources, DynaMICE projected 253 million measles cases, 3.8 million deaths and 233 million DALYs incurred over 2000–2050 in the ten high-burden countries when MCV1, MCV2, and SIA doses were implemented. Compared to no vaccination, MCV1 contributed to 66% reduction in cumulative measles cases, while MCV2 and SIAs reduced this further to 90%. Among the updated determinants, shifting from fixed to linearly-varying vaccine efficacy by age and from static to time-varying case-fatality risks had the biggest effect on MCV impact. While varying the basic reproduction number showed a limited effect, updates on the other four determinants together resulted in an overall reduction of vaccination impact by 0.58%, 26.2%, and 26.7% for cases, deaths, and DALYs averted, respectively. COVID-19 related disruptions to measles vaccination are not likely to change the influence of these determinants on MCV impact, but may lead to a 3% increase in cases over 2000–2050. Conclusions Incorporating updated evidence particularly on vaccine efficacy and case-fatality risk reduces estimates of vaccination impact moderately, but its overall impact remains considerable. High MCV coverage through both routine immunisation and SIAs remains essential for achieving and maintaining low incidence in high measles burden settings.

scholarly journals Graphs with specified degree distributions, simple epidemics, and local vaccination strategies

2007 ◽  
Vol 39 (4) ◽  
pp. 922-948 ◽  
Author(s):  
Tom Britton ◽  
Svante Janson ◽  
Anders Martin-Löf
Keyword(s):  
Infectious Disease ◽  
Social Structure ◽  
Basic Reproduction Number ◽  
Degree Distribution ◽  
Reproduction Number ◽  
Final Size ◽  
Vaccination Strategies ◽  
The Social ◽  
Major Outbreak ◽  
The Basic Reproduction Number

Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R0, the basic reproduction number, and τ0, the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine Rv, the reproduction number, and τv, the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.

scholarly journals Community structured model for vaccine strategies to control COVID19 spread: a mathematical study

2021 ◽  
Author(s):  
Elena Aruffo ◽  
Pei Yuan ◽  
Yi Tan ◽  
Evgenia Gatov ◽  
Effie Gournis ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Compartment Model ◽  
Effective Vaccine ◽  
Household Transmission ◽  
Waning Immunity ◽  
Vaccine Distribution ◽  
The Impact ◽  
The Basic Reproduction Number

AbstractEfforts to mitigate the COVID-19 pandemic have relied heavily on non-pharmaceutical interventions (NPIs), including physical distancing, hand hygiene, and mask-wearing. However, an effective vaccine is essential to containing the spread of the virus. The first doses were distributed at the end of 2020, but the efficacy, period of immunity it will provide, and percentage of coverage still remain unclear. We developed a compartment model to examine different vaccine strategies for controlling the spread of COVID-19. Our framework accounts for testing rates, test-turnaround times, and vaccination waning immunity. Using reported case data from the city of Toronto, Canada between Mar-Dec, 2020 we defined epidemic phases of infection using contact rates, which depend on individuals’ duration of time spent within the household, workplace/school, or community settings, as well as the probability of transmission upon contact. We investigated the impact of vaccine distribution by comparing different permutations of waning immunity, vaccine coverage and efficacy throughout various stages of NPI’s relaxation in terms of cases, deaths, and household transmission, as measured using the basic reproduction number (R0). We observed that widespread vaccine coverage substantially reduced the number of cases and deaths. In order for NPIs to be relaxed 8 months after vaccine distribution, infection spread can be kept under control with either 60% vaccine coverage, no waning immunity, and 70% efficacy, or with 60% coverage with a 12-month waning immunity and 90% vaccine efficacy. Widespread virus resurgence can result when the immunity wanes under 3 months and/or when NPI’s are relaxed in concomitance with vaccine distribution. In addition to vaccination, our analysis of R0 showed that the basic reproduction number is reduced by decreasing the tests turnaround time and transmission in the household. While we found that household transmission can decrease following the introduction of a vaccine, public health efforts to reduce test turnaround times remain important for virus containment. Our findings suggest that vaccinating two-thirds of the population with a vaccine that is at least 70% effective may be sufficient for controlling COVID-19 spread, as long as NPI’s are not immediately relaxed.

scholarly journals Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population

2010 ◽  
Vol 7 (52) ◽  
pp. 1537-1544 ◽  
Author(s):  
Michiel van Boven ◽  
Mirjam Kretzschmar ◽  
Jacco Wallinga ◽  
Philip D O'Neill ◽  
Ole Wichmann ◽  
...  
Keyword(s):  
Public School ◽  
Vaccination Coverage ◽  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Credible Interval ◽  
Final Size ◽  
Measles Elimination ◽  
The Basic Reproduction Number

Measles is a highly infectious disease that has been targeted for elimination from four WHO regions. Whether and under which conditions this goal is feasible is, however, uncertain since outbreaks have been documented in populations with high vaccination coverage (more than 90%). Here, we use the example of a large outbreak in a German public school to show how estimates of key epidemiological parameters such as the basic reproduction number ( R 0 ), vaccine efficacy (VE S ) and critical vaccination coverage ( p c ) can be obtained from partially observed outbreaks in highly vaccinated populations. Our analyses rely on Bayesian methods of inference based on the final size distribution of outbreak size, and use data which are easily collected. For the German public school the analyses indicate that the basic reproduction number of measles is higher than previously thought ( , 95% credible interval: 23.6–40.4), that the vaccine is highly effective in preventing infection ( , 95% credible interval: 0.993–0.999), and that a vaccination coverage in excess of 95 per cent may be necessary to achieve herd immunity ( , 95% credible interval: 0.961–0.978). We discuss the implications for measles elimination from highly vaccinated populations.

scholarly journals Predicting Required COVID-19 Vaccine Coverage and its Impact in Sierra Leone Using Mathematical models

2021 ◽  
Author(s):  
Abdul A. Kamara ◽  
Joseph A. L. Kamara ◽  
Sallieu K. Samura
Keyword(s):  
Mathematical Models ◽  
Explicit Formula ◽  
Sierra Leone ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Transmission Rate ◽  
Asymptomatic Infection ◽  
The Impact ◽  
The Basic Reproduction Number

Abstract In this article, we predict the required vaccine coverage to eradicate the COVID-19 outbreak in Sierra Leone. We also, investigate the impact of facemask and vaccine coverage on the spread of the COVID-19 virus using a modified symptomatic-asymptomatic infection transmissions Susceptible-Latent-Infectious-Asymptomatic-Recovered (SLIAR) model. We derived an explicit formula for the basic reproduction number and used it to understand the dynamics of the disease when it is greater than unity. Numerically, we show that 58 per cent of the Sierra Leone national population required vaccination to eradicate the COVID-19 virus. Also, the SLIAR with vaccine model results reveal that the impact of using facemask is very challenging to understand and the vaccine coverage decrease the infected transmission rate but cannot completely eradicate the infection.

scholarly journals Modeling Saturated Diagnosis and Vaccination in Reducing HIV/AIDS Infection

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Can Chen ◽  
Yanni Xiao
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Drug Users ◽  
Yunnan Province ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Vaccination Rate ◽  
Manifold Theory ◽  
The Basic Reproduction Number ◽  
Hiv Aids

A mathematical model is proposed to consider the effects of saturated diagnosis and vaccination on HIV/AIDS infection. By employing center manifold theory, we prove that there exists a backward bifurcation which suggests that the disease cannot be eradicated even if the basic reproduction number is less than unity. Global stability of the disease-free equilibrium is investigated for appropriate conditions. When the basic reproduction number is greater than unity, the system is uniformly persistent. The proposed model is applied to describe HIV infection among injecting drug users (IDUs) in Yunnan province, China. Numerical studies indicate that new cases and prevalence are sensitive to transmission rate, vaccination rate, and vaccine efficacy. The findings suggest that increasing vaccination rate and vaccine efficacy and enhancing interventions like reducing share injectors can greatly reduce the transmission of HIV among IDUs in Yunnan province, China.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Impact of early detection and vaccination strategy in COVID-19 eradication program in Jakarta, Indonesia

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Dipo Aldila ◽  
Brenda M. Samiadji ◽  
Gracia M. Simorangkir ◽  
Sarbaz H. A. Khosnaw ◽  
Muhammad Shahzad
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Vaccination Strategy ◽  
Vaccination Rate ◽  
Rapid Testing ◽  
Social Distancing ◽  
Rapid Spread ◽  
Vaccine Potential ◽  
The Basic Reproduction Number

Abstract Objective Several essential factors have played a crucial role in the spreading mechanism of COVID-19 (Coronavirus disease 2019) in the human population. These factors include undetected cases, asymptomatic cases, and several non-pharmaceutical interventions. Because of the rapid spread of COVID-19 worldwide, understanding the significance of these factors is crucial in determining whether COVID-19 will be eradicated or persist in the population. Hence, in this study, we establish a new mathematical model to predict the spread of COVID-19 considering mentioned factors. Results Infection detection and vaccination have the potential to eradicate COVID-19 from Jakarta. From the sensitivity analysis, we find that rapid testing is crucial in reducing the basic reproduction number when COVID-19 is endemic in the population rather than contact trace. Furthermore, our results indicate that a vaccination strategy has the potential to relax social distancing rules, while maintaining the basic reproduction number at the minimum possible, and also eradicate COVID-19 from the population with a higher vaccination rate. In conclusion, our model proposed a mathematical model that can be used by Jakarta’s government to relax social distancing policy by relying on future COVID-19 vaccine potential.

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