scholarly journals Herd Immunity in India: A Review

2021 ◽  
Vol 3 (1) ◽  
pp. 18-21
Author(s):  
Sheema Fatima Khan
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Natural Infection ◽  
Herd Immunity ◽  
Herd Effect ◽  
Susceptible Population ◽  
Herd Protection ◽  
Cdc Guidelines ◽  
And Control

Herd Immunity is a brilliant solution to tackle and control global pandemics, if taken proper route for immunization such as through vaccination. It is defined as the number of immune individuals against a transmissible virus in a completely susceptible population. The term herd protection or herd effect is the protection to the whole population due to herd immunity. Herd immunity threshold is the minimum proportion of immune population required for herd effect or herd protection. To calculate the threshold, we use basic reproduction number (R0) to measure the rate of transmission of pathogen, in this case SARS-CoV-2. However, a better measure is effective reproduction number (Re). India is major example of herd immunity. Despite strict lockdown and other Covid measure, due to already crowded area the virus could spread fast and to vast majority of people if one of them were to catch it. This explains the steady decline in the number of coronavirus cases in India. At the end, until an approved effective vaccination available, public will still need to follow all the CDC guidelines in order to avoid the large deaths along with natural infection.

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 Global Stability and Sensitivity Assessment of COVID-19 with Timely and Delayed Diagnosis in Ghana

2021 ◽  
Author(s):  
Stephen E. Moore ◽  
Hetsron L. Nyandjo Bamen ◽  
Joshua Kiddy K. Asamoah ◽  
Olivier Menoukeu-Pamen ◽  
Zhen Jin
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Delayed Diagnosis ◽  
Rank Correlation ◽  
Health Benefit ◽  
Recruitment Rate ◽  
Susceptible Population ◽  
Sensitivity Assessment ◽  
Reported Data ◽  
The Basic Reproduction Number

Abstract In this paper, we present the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana, using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, R_0, for the proposed model is 1.04. One of the main focus of this study is stability results and senesitity assessment of the parameters. We show both theoretically and numerically that, the disease can be eliminated when the basic reproduction number is less or equal to a unity. Furthermore, we show that the disease persist whenever R_0>1 or whenever there is a delay in the diagnoses of infected individuals in the community. To assess the most influential parameters in the basic reproduction number, we carried out global sensitivity analysis. The scatter plots and the partial rank correlation coefficient reveal that, the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility of exposed individuals; and that the most negative sensitive parameters are the proportion of the infectious with timely diagnosis, and the transition rate of self-quarantined individuals to the susceptible population. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection).

scholarly journals Covid 19: Need of vaccine induced herd immunity in India

2020 ◽  
Vol 2 (4) ◽  
pp. 82-84
Author(s):  
D. Pragathi ◽  
Dinesh Kumar Kukunuri ◽  
Venkatesh Paturu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Traditional Concept ◽  
Contagious Diseases ◽  
Research Article ◽  
Past Data ◽  
The Mean ◽  
Novel Coronavirus ◽  
Indirect Protection

Introduction: Herd immunity is a traditional concept nothing but a form of indirect protection from contagious diseases. In a mass community, there is no need to be everyone immune. If a high proportion of members in the community are immune, spreading of the disease is reduced even to non-immunized patients. This study offers an overview of vaccine-induced herd immunity importance in this pandemic and how it will be achieved. Methodology: The data of basic reproduction number Ro values for COVID 19 of 10 weeks in India which were estimated by Ro package in R software are extracted from a research article (reference no.4) and taken the mean Ro value due to fluctuations as well as to avoid great errors by using MS Excel. Herd immunity is calculated by using a standard equation stated as R=(1-Pc )(1-P1)Ro   Results:  The mean basic reproduction number Ro for COVID 19 in India was calculated as 1.671 by using MS excel and the herd 3 determines that only 40.16% proportion of individuals need to immunized through a vaccine to achieve herd immunity towards COVID 19 in India. Conclusion: This study estimates mean base reproduction Ro as 1.671 and Herd Immunity Threshold (HIT) as 40.16% by using past data. This study concludes that vaccine-induced herd immunity helps us by playing a key role to eliminate novel coronavirus.

scholarly journals Sustainable social distancing through facemask use and testing during the Covid-19 pandemic

2020 ◽  
Author(s):  
Diego Chowell ◽  
Kimberlyn Roosa ◽  
Ranu Dhillon ◽  
Gerardo Chowell ◽  
Devabhaktuni Srikrishna
Keyword(s):  
Basic Reproduction Number ◽  
Symptom Onset ◽  
Social Protection ◽  
Reproduction Number ◽  
Type Model ◽  
Protective Behaviors ◽  
Social Distancing ◽  
And Control ◽  
Different Levels ◽  
The Basic Reproduction Number

We investigate how individual protective behaviors, different levels of testing, and isolation influence the transmission and control of the COVID-19 pandemic. Based on an SEIR-type model incorporating asymptomatic but infectious individuals (40%), we show that the pandemic may be readily controllable through a combination of testing, treatment if necessary, and self-isolation after testing positive (TTI) of symptomatic individuals together with social protection (e.g., facemask use, handwashing). When the basic reproduction number, R0, is 2.4, 65% effective social protection alone (35% of the unprotected transmission) brings the R below 1. Alternatively, 20% effective social protection brings the reproduction number below 1.0 so long as 75% of the symptomatic population is covered by TTI within 12 hours of symptom onset. Even with 20% effective social protection, TTI of 1 in 4 symptomatic individuals can substantially 'flatten the curve' cutting the peak daily incidence in half.

scholarly journals Mathematical model of transmission dynamics with mitigation and health measures for SARS-CoV-2 infection in European countries

2020 ◽  
Author(s):  
Shweta Sankhwar ◽  
Narender Kumar ◽  
Ravins Dohare
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
European Countries ◽  
Transmission Dynamics ◽  
Second Phase ◽  
Geographical Regions ◽  
Two Phases ◽  
Spread Of Infection ◽  
And Control

Abstract The pandemic of Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV-2) continue to pose a serious threat to global health resulting in disease COVID-19. No specific drug or vaccine is available against this infection. Therefore, the prevention is only way to reduce the spread of infection. The pandemic needs an enhanced mathematical model, therefore, we propose a SEIAJR compartmental mathematical model to estimate the basic reproduction number (R0 ) and the transmission dynamics of four European countries (Germany, United Kingdom, Switzerland and Spain). The proposed mathematical model incorporates mitigation and healthcare measures as recommended by ECDC (European Centre for Disease Prevention and Control). The simulation of proposed model is done in two phases. First-phase simulation estimates basic reproduction number and mitigation rate according to active infected cases in all four European countries. R0 estimate 2.82 - 3.3 for considered European countries. Second-phase simulation predicts the dynamics of infection on the estimated R0 with varying mitigation rate and constant healthcare rate. This study predicts that no more mitigation is required to invade the infection. The current mitigation and healthcare measures are enough to stop the propogation of infection, however, infection would last by end of July 2020. The developed mathematical model would also be applicable to portray the infection trasmission dynamics for other geographical regions with varying parameters.

An early estimation of the number of affected people in South Asia due to Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (10) ◽  
pp. 2050140
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
South Asia ◽  
South Asian ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model ◽  
Asian Countries ◽  
Susceptible Population ◽  
The Basic Reproduction Number

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case in Pakistan due to the SARS-CoV-2 will be comparable with that in China whereas it will be low for Bangladesh and India. The basic reproduction number, with fluctuations, for South Asian countries are predicted to be less than that of China. The susceptible population is also estimated to be under a million for Bangladesh and India but it becomes very large for Pakistan.

scholarly journals Dengue disease, basic reproduction number and control

2012 ◽  
Vol 89 (3) ◽  
pp. 334-346 ◽  
Author(s):  
Helena Sofia Rodrigues ◽  
M. Teresa T. Monteiro ◽  
Delfim F. M. Torres ◽  
Alan Zinober
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Dengue Disease ◽  
And Control

scholarly journals The spatial transmission of SARS-CoV-2 in China under the prevention and control measures at the early outbreak

2021 ◽  
Vol 79 (1) ◽  
Author(s):  
Jianli Liu ◽  
Yuan Zhou ◽  
Chuanyu Ye ◽  
Guangming Zhang ◽  
Feng Zhang ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Prevention And Control ◽  
Reproduction Number ◽  
Early Stage ◽  
Chinese Mainland ◽  
Hubei Province ◽  
Control Measures ◽  
Provincial Level ◽  
Prevention And Control Measures ◽  
And Control

Abstract Background Since severe acute respiratory syndrome coronavirus, 2 (SARS-CoV-2) was firstly reported in Wuhan City, China in December 2019, Novel Coronavirus Disease 2019 (COVID-19) that is caused by SARS-CoV-2 is predominantly spread from person-to-person on worldwide scales. Now, COVID-19 is a non-traditional and major public health issue the world is facing, and the outbreak is a global pandemic. The strict prevention and control measures have mitigated the spread of SARS-CoV-2 and shown positive changes with important progress in China. But prevention and control tasks remain arduous for the world. The objective of this study is to discuss the difference of spatial transmission characteristics of COVID-19 in China at the early outbreak stage with resolute efforts. Simultaneously, the COVID-19 trend of China at the early time was described from the statistical perspective using a mathematical model to evaluate the effectiveness of the prevention and control measures. Methods In this study, the accumulated number of confirmed cases publicly reported by the National Health Committee of the People’s Republic of China (CNHC) from January 20 to February 11, 2020, were grouped into three partly overlapping regions: Chinese mainland including Hubei province, Hubei province alone, and the other 30 provincial-level regions on Chinese mainland excluding Hubei province, respectively. A generalized-growth model (GGM) was used to estimate the basic reproduction number to evaluate the transmissibility in different spatial locations. The prevention and control of COVID-19 in the early stage were analyzed based on the number of new cases of confirmed infections daily reported. Results Results indicated that the accumulated number of confirmed cases reported from January 20 to February 11, 2020, is well described by the GGM model with a larger correlation coefficient than 0.99. When the accumulated number of confirmed cases is well fitted by an exponential function, the basic reproduction number of COVID-19 of the 31 provincial-level regions on the Chinese mainland, Hubei province, and the other 30 provincial-level regions on the Chinese mainland excluding Hubei province, is 2.68, 6.46 and 2.18, respectively. The consecutive decline of the new confirmed cases indicated that the prevention and control measures taken by the Chinese government have contained the spread of SARS-CoV-2 in a short period. Conclusions The estimated basic reproduction number thorough GGM model can reflect the spatial difference of SARS-CoV-2 transmission in China at the early stage. The strict prevention and control measures of SARS-CoV-2 taken at the early outbreak can effectively reduce the new confirmed cases outside Hubei and have mitigated the spread and yielded positive results since February 2, 2020. The research results indicated that the outbreak of COVID-19 in China was sustaining localized at the early outbreak stage and has been gradually curbed by China’s resolute efforts.

scholarly journals Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

2021 ◽  
Author(s):  
Jayanta Kumar Ghosh ◽  
Prahlad Majumdar ◽  
Uttam Ghosh
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Logistic Growth ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Susceptible Population ◽  
Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

scholarly journals Vaccination is Australia's most important COVID-19 public health action, even though herd immunity is unlikely

2021 ◽  
Author(s):  
Emma S McBryde ◽  
Michael T Meehan ◽  
Jamie Sziklay ◽  
Adeshina Adekunle ◽  
Abdul Kuddus ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Severe Disease ◽  
Herd Immunity ◽  
Public Health Action ◽  
Herd Protection ◽  
Health Action ◽  
The Impact ◽  
Indirect Protection ◽  
Better Than

The Australian National Cabinet four-step plan to transition to post-pandemic re-opening begins with vaccination to achieve herd protection and protection of the health system against a surge in COVID-19 cases. Assuming a pre-vaccination reproduction number for the Delta variant of 5, we show that for the current Mixed program of vaccinating over 60s with AstraZeneca and 16-60s with Pfizer we would not achieve herd immunity. We would need to cover 85% of the population (including many 5-16 year-olds to achieve herd immunity). At lower reproduction number of 3 and our current Mixed strategy, we can achieve herd immunity without vaccinating 5-15 year olds. This will be achieved at a 60% coverage pursuing a strategy targetting high transmitters or 70% coverage using a strategy targetting the vulnerable first. A reproduction number of 7 precludes achieving herd immunity, however vaccination is able to prevent 75% of deaths compared with no vaccination. We also examine the impact of vaccination on death in the event that herd immunity is not achieved. Direct effects of vaccination on reducing death are very good for both Pfizer and AstraZeneca vaccines. However we estimate that the Mixed or Pfizer program performs better than the AstraZeneca program. Furthermore, vaccination levels below the herd immunity threshold can lead to substantial (albeit incomplete) indirect protection for both vaccinated and unvaccinated populations. Given the potential for not reaching herd immunity, we need to consider what level of severe disease and death is acceptable, balanced against the consequences of ongoing aggressive control strategies.

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