scholarly journals Herd immunity of Covid 19 in dynamic environments with vaccination: a model based study

2020 ◽  
Author(s):  
Liwei Yang ◽  
Bochuan Chen ◽  
Yu Zhang ◽  
Siyao Du ◽  
Lang Zhao
Keyword(s):  
Reproduction Number ◽  
Disease Model ◽  
Herd Immunity ◽  
Dynamic Environment ◽  
Potential Effect ◽  
Third Wave ◽  
Social Distancing ◽  
Infectious Disease Model ◽  
Intervention Measures ◽  
Combined Intervention

Abstract BackgroundThe first wave of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Canada is entering the last stage, while the development of vaccine is still ongoing. A thorough analysis on the potential effect of restoring to the normal life was needed.MethodsWe used an infectious disease model which optimized for individual immunity to investigate the potential impact of the vaccine on the number of cases, ℛ𝑡, and the duration of the epidemic. We modeled the severity of the cases with three intervention measures and the effect of herd immunity. The combined intervention strategies with the vaccination, speed of vaccination, and the proportion of population pre-vaccinated before reopening were modeled to give an overview of the effect of the vaccination. For each simulation, we set the observation range to be from Feb, 2020 to Oct. 2021, and modeled the number of cases after the first wave, the change of reproduction number (ℛ𝑡), and the proportion of immunized population under the effect of waning immunity.FindingsWe found the proportion of immunized population to reach herd immunity in a dynamic environment to be between 1−1ℛ0and 1−1ℛ02; for Covid-19, the threshold proportion is 64·16%, the final proportion of infections could be up to 87·15% when basic reproduction number (ℛ0) is 2·79. The average number of cases predicted in Canada after the first wave was 285590, 90260, 163057, and 60082 with no intervention, social distancing, quarantining severe cases, and combined strategies; 122261, 89903, 49276, 39856, and 10983 cases with 0·1%, 0·2%, 0·3%, 0·4%, and 1·0% of the population vaccinated per day; 117475, 93502, 91634, 79418, and 8713 cases with 10%, 20%, 30%, 40%, and 50% of population immunized before reopening. Assuming the half-life of the effectivity of the antibody is 48 weeks for symptomatic cases, 24 weeks for asymptomatic cases.Interpretation Neither of these strategies cannot prevent the second wave solely nor together. However, the third wave can be prevented with both social distancing and quarantining severe cases in practice. The speed and timing of vaccination has a direct impact on the reduction of the final number of cases. Unexpectedly, the proportion of population immunized before reopening did not lead to a huge shift of the number of cases after the first wave when the immunized proportion is lower than the critical proportion (49·6%) when social distancing is in practice.

scholarly journals CoMix: comparing mixing patterns in the Belgian population during and after lockdown

2020 ◽  
Author(s):  
Pietro Coletti ◽  
James Wambua ◽  
Amy Gimma ◽  
Lander Willem ◽  
Sarah Vercruysse ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Communicable Disease ◽  
Age Classes ◽  
Personal Protection Equipment ◽  
Social Distancing ◽  
Intervention Measures ◽  
System Collapse ◽  
Contact Behaviour ◽  
Hygienic Measures ◽  
Belgian Population

AbstractBackgroundThe COVID-19 pandemic has shown how a newly emergent communicable disease can lay considerable burden on public health. To avoid system collapse, governments have resorted to several social distancing measures. In Belgium, this included a lockdown and a following period of phased re-opening.MethodsA representative sample of Belgian adults was asked about their contact behaviour from mid-April to the beginning of August, during different stages of the intervention measures in Belgium. Use of personal protection equipment (face masks) and compliance to hygienic measures was also reported. We estimated the expected reproduction number computing the ratio of R0 with respect to pre-pandemic data.FindingsDuring the first two waves (the first month) of the survey, the reduction in the average number of contacts was around 80% and was quite consistent across all age-classes. The average number of contacts increased over time, particularly for the younger age classes, still remaining significantly lower than pre-pandemic values. From the end of May to the end of July, the estimated reproduction number has a median value larger than one, although with a wide dispersion. Estimated 0 fell below one again at the beginning of August.ConclusionsWe have shown how a rapidly deployed survey can measure compliance to social distancing and assess its impact on COVID-19 spread. Monitoring the effectiveness of social distancing recommendations is of paramount importance to avoid further waves of COVID-19.

scholarly journals CoMix: comparing mixing patterns in the Belgian population during and after lockdown

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Pietro Coletti ◽  
James Wambua ◽  
Amy Gimma ◽  
Lander Willem ◽  
Sarah Vercruysse ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Communicable Disease ◽  
Age Classes ◽  
Personal Protection Equipment ◽  
Social Distancing ◽  
Intervention Measures ◽  
System Collapse ◽  
Contact Behaviour ◽  
Hygienic Measures ◽  
Belgian Population

AbstractThe COVID-19 pandemic has shown how a newly emergent communicable disease can lay considerable burden on public health. To avoid system collapse, governments have resorted to several social distancing measures. In Belgium, this included a lockdown and a following period of phased re-opening. A representative sample of Belgian adults was asked about their contact behaviour from mid-April to the beginning of August, during different stages of the intervention measures in Belgium. Use of personal protection equipment (face masks) and compliance to hygienic measures was also reported. We estimated the expected reproduction number computing the ratio of $$\hbox {R}_{0}$$ R 0 with respect to pre-pandemic data. During the first two waves (the first month) of the survey, the reduction in the average number of contacts was around 80% and was quite consistent across all age-classes. The average number of contacts increased over time, particularly for the younger age classes, still remaining significantly lower than pre-pandemic values. From the end of May to the end of July , the estimated reproduction number has a median value larger than one, although with a wide dispersion. Estimated $$\hbox {R}_{0}$$ R 0 fell below one again at the beginning of August. We have shown how a rapidly deployed survey can measure compliance to social distancing and assess its impact on COVID-19 spread. Monitoring the effectiveness of social distancing recommendations is of paramount importance to avoid further waves of COVID-19.

Modeling and Analysis of an Imprecise Epidemic System with Optimal Treatment and Vaccination Control

2018 ◽  
Vol 13 (02) ◽  
pp. 37-60
Author(s):  
Anjana Das ◽  
M. Pal
Keyword(s):  
Infectious Disease ◽  
Functional Form ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Disease Model ◽  
Control Parameters ◽  
Interval Numbers ◽  
Modeling And Analysis ◽  
Infectious Disease Model ◽  
Imprecise Parameters

In this paper, we propose and analyze a Susceptible-Vaccinated-Exposed-Infected-Recovered (SVEIR) type infectious disease model with imprecise parameters. Introducing the interval numbers in functional form, the SVEIR model is proposed and formulated. The existence of possible equilibrium points with their feasibility criteria and an explicit value of basic reproduction number is obtained. The asymptotic stability of the system at different equilibrium points are also discussed. Next by considering treatment and vaccination as two control parameters, an optimal control problem is formulated and solved. Finally, some computer simulation works are given in support of our analytical results.

scholarly journals Effect of Alert Level 4 on Reff: review of international COVID-19 cases

2020 ◽  
Author(s):  
Rachelle N. Binny ◽  
Shaun C. Hendy ◽  
Alex James ◽  
Audrey Lustig ◽  
Michael J. Plank ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Late Phase ◽  
List Type ◽  
Executive Summary ◽  
Social Distancing ◽  
Transmission Potential ◽  
A Value ◽  
Intervention Measures ◽  
Level 3 ◽  
Case Data

AbstractThe effective reproduction number, Reff, is an important measure of transmission potential in the modelling of epidemics. It measures the average number of people that will be infected by a single contagious individual. A value of Reff > 1 suggests that an outbreak will occur, while Reff < 1 suggests the virus will die out. In response to the COVID-19 pandemic, countries worldwide are implementing a range of intervention measures, such as population-wide social distancing and case isolation, with the goal of reducing Reff to values below one, to slow or eliminate transmission. We analyse case data from 25 international locations to estimate their Reff values over time and to assess the effectiveness of interventions, equivalent to New Zealand’s Alert Levels 1-4, for reducing transmission. Our results show that strong interventions, equivalent to NZ’s Alert Level 3 or 4, have been successful at reducing Reff below the threshold for outbreak. In general, countries that implemented strong interventions earlier in their outbreak have managed to maintain case numbers at lower levels. These estimates provide indicative ranges of Reff for each Alert Level, to inform parameters in models of COVID-19 spread under different intervention scenarios in New Zealand and worldwide. Predictions from such models are important for informing policy and decisions on intervention timing and stringency during the pandemic.Executive SummaryIn response to the COVID-19 pandemic, countries around the world are implementing a range of intervention measures, such as population-wide social distancing and case isolation, with the goal of reducing the spread of the virus.Reff, the effective reproduction number, measures the average number of people that will be infected by a single contagious individual. A value of Reff > 1 suggests that an outbreak will occur, while Reff < 1 suggests the virus will die out.Comparing Reff in an early outbreak phase (no or low-level interventions implemented) with a later phase (moderate to high interventions) indicates how effective these measures are for reducing Reff.We estimate early-phase and late-phase Reff values for COVID-19 outbreaks in 25 countries (or provinces/states). Results suggest interventions equivalent to NZ’s Alert Level 3-4 can successfully reduce Reff below the threshold for outbreak.

scholarly journals Role of Mathematical Model in Curbing COVID-19 in Nigeria

2021 ◽  
Vol 3 (2) ◽  
pp. 135-147
Author(s):  
Chinwendu Emilian Madubueze ◽  
Nkiru Maria Akabuike ◽  
Sambo Dachollom
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Viral Disease ◽  
Control Measures ◽  
Social Distancing ◽  
Testing Rate ◽  
Intervention Measures ◽  
The Impact ◽  
The Basic Reproduction Number

COVID-19 is a viral disease that is caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARSCoV-2) which has no approved vaccine. Based on the available non-pharmacological interventions like wearing of face masks, observing social distancing, and lockdown, this work assesses the impact of non-pharmaceutical control measures (social distancing and use of face-masks) and mass testing on the transmission of COVID-19 in Nigeria. A mathematical model for COVID-19 is formulated with intervention measures (observing social distancing and wearing of face masks) and mass testing. The basic reproduction number, R_0, is computed using next-generation method while the disease-free equilibrium is found to be locally and globally asymptotically stable when R_0< 1. The model is parameterized using Nigeria data on COVID-19 in Nigeria. The basic reproduction number is found to be less than unity (R_0 < 1) either when the compliance with intervention measures is moderate (50% <= alpha< 70%) and the testing rate per day is moderate (0,5 <=alpha_2 < 0,7) or when the compliance with intervention measures is strict (alpha>=70%) and the testing rate per day is poor (alpha_2 = 0,3). This implies that Nigeria will be able to halt the spread of COVID-19 under these two conditions. However, it will be easier to enforce strict compliance with intervention measures in the presence of poor testing rate due to the limited availability of testing facilities and manpower in Nigeria. Hence, this study advocates that Nigerian governments (Federal and States) should aim at achieving a testing rate of at least 0.3 per day while ensuring that all the citizens strictly comply with wearing face masks and observing social distancing in public.

scholarly journals Public Compliance With Social Distancing Measures and SARS-CoV-2 Spread

2021 ◽  
pp. 003335492110112
Author(s):  
Hongjie Liu ◽  
Chang Chen ◽  
Raul Cruz-Cano ◽  
Jennifer L. Guida ◽  
Minha Lee
Keyword(s):  
Growth Rate ◽  
Reproduction Number ◽  
Early Stage ◽  
Human Mobility ◽  
The United States ◽  
Density Change ◽  
Regression Coefficients ◽  
Daily Growth Rate ◽  
Daily Growth ◽  
Social Distancing

Objective We quantified the association between public compliance with social distancing measures and the spread of SARS-CoV-2 during the first wave of the epidemic (March–May 2020) in 5 states that accounted for half of the total number of COVID-19 cases in the United States. Methods We used data on mobility and number of COVID-19 cases to longitudinally estimate associations between public compliance, as measured by human mobility, and the daily reproduction number and daily growth rate during the first wave of the COVID-19 epidemic in California, Illinois, Massachusetts, New Jersey, and New York. Results The 5 states mandated social distancing directives during March 19-24, 2020, and public compliance with mandates started to decrease in mid-April 2020. As of May 31, 2020, the daily reproduction number decreased from 2.41-5.21 to 0.72-1.19, and the daily growth rate decreased from 0.22-0.77 to –0.04 to 0.05 in the 5 states. The level of public compliance, as measured by the social distancing index (SDI) and daily encounter-density change, was high at the early stage of implementation but decreased in the 5 states. The SDI was negatively associated with the daily reproduction number (regression coefficients range, –0.04 to –0.01) and the daily growth rate (from –0.009 to –0.01). The daily encounter-density change was positively associated with the daily reproduction number (regression coefficients range, 0.24 to 1.02) and the daily growth rate (from 0.05 to 0.26). Conclusions Social distancing is an effective strategy to reduce the incidence of COVID-19 and illustrates the role of public compliance with social distancing measures to achieve public health benefits.

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.

scholarly journals Effectiveness of Face Masks in Reducing the Spread of COVID-19: A Model-Based Analysis

2021 ◽  
pp. 0272989X2110190
Author(s):  
Isabelle J. Rao ◽  
Jacqueline J. Vallon ◽  
Margaret L. Brandeau
Keyword(s):  
New York ◽  
Infected Individual ◽  
Disease Model ◽  
World Health ◽  
Sensitivity Analyses ◽  
Reproductive Number ◽  
Social Distancing ◽  
Health Organization ◽  
Almost All ◽  
Mask Effectiveness

Background The World Health Organization and US Centers for Disease Control and Prevention recommend that both infected and susceptible people wear face masks to protect against COVID-19. Methods We develop a dynamic disease model to assess the effectiveness of face masks in reducing the spread of COVID-19, during an initial outbreak and a later resurgence, as a function of mask effectiveness, coverage, intervention timing, and time horizon. We instantiate the model for the COVID-19 outbreak in New York, with sensitivity analyses on key natural history parameters. Results During the initial epidemic outbreak, with no social distancing, only 100% coverage of masks with high effectiveness can reduce the effective reproductive number [Formula: see text] below 1. During a resurgence, with lowered transmission rates due to social distancing measures, masks with medium effectiveness at 80% coverage can reduce [Formula: see text] below 1 but cannot do so if individuals relax social distancing efforts. Full mask coverage could significantly improve outcomes during a resurgence: with social distancing, masks with at least medium effectiveness could reduce [Formula: see text] below 1 and avert almost all infections, even with intervention fatigue. For coverage levels below 100%, prioritizing masks that reduce the risk of an infected individual from spreading the infection rather than the risk of a susceptible individual from getting infected yields the greatest benefit. Limitations Data regarding COVID-19 transmission are uncertain, and empirical evidence on mask effectiveness is limited. Our analyses assume homogeneous mixing, providing an upper bound on mask effectiveness. Conclusions Even moderately effective face masks can play a role in reducing the spread of COVID-19, particularly with full coverage, but should be combined with social distancing measures to reduce [Formula: see text] below 1. [Box: see text]

scholarly journals The challenges of containing SARS-CoV-2 via test-trace-and-isolate

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sebastian Contreras ◽  
Jonas Dehning ◽  
Matthias Loidolt ◽  
Johannes Zierenberg ◽  
F. Paul Spitzner ◽  
...  
Keyword(s):  
Analytical Model ◽  
Reproduction Number ◽  
Tipping Points ◽  
Social Distancing ◽  
Promising Tool

AbstractWithout a cure, vaccine, or proven long-term immunity against SARS-CoV-2, test-trace-and-isolate (TTI) strategies present a promising tool to contain its spread. For any TTI strategy, however, mitigation is challenged by pre- and asymptomatic transmission, TTI-avoiders, and undetected spreaders, which strongly contribute to ”hidden" infection chains. Here, we study a semi-analytical model and identify two tipping points between controlled and uncontrolled spread: (1) the behavior-driven reproduction number $${R}_{t}^{H}$$ R t H of the hidden chains becomes too large to be compensated by the TTI capabilities, and (2) the number of new infections exceeds the tracing capacity. Both trigger a self-accelerating spread. We investigate how these tipping points depend on challenges like limited cooperation, missing contacts, and imperfect isolation. Our results suggest that TTI alone is insufficient to contain an otherwise unhindered spread of SARS-CoV-2, implying that complementary measures like social distancing and improved hygiene remain necessary.

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