scholarly journals Epidemiology of the Zika virus outbreak in the Cabo Verde Islands, West Africa

2017 ◽  
Author(s):  
José Lourenço ◽  
Maria de Lourdes Monteiro ◽  
Tomás Valdez ◽  
Júlio Monteiro Rodrigues ◽  
Oliver G. Pybus ◽  
...  
Keyword(s):  
West Africa ◽  
Zika Virus ◽  
Attack Rate ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Framework ◽  
Single Wave ◽  
Cabo Verde ◽  
Small Observation

AbstractIntroductionThe Zika virus (ZIKV) outbreak in the island nation of Cabo Verde was of unprecedented magnitude in Africa and the first to be associated with microcephaly in the continent.MethodsUsing a simple mathematical framework we present a first epidemiological assessment of attack and observation rates from 7,580 ZIKV notified cases and 18 microcephaly reports between July 2015 and May 2016.ResultsIn line with observations from the Americas and elsewhere, the single-wave Cabo Verdean ZIKV epidemic was characterized by a basic reproductive number of 1.85 (95% CI, 1.5 −2.2), with overall the attack rate of 51.1% (range 42.1 - 61.1) and observation rate of 2.7% (range 2.29 - 3.33).ConclusionCurrent herd-immunity may not be sufficient to prevent future small-to-medium epidemics in Cabo Verde. Together with a small observation rate, these results highlight the need for rapid and integrated epidemiological, molecular and genomic surveillance to tackle forthcoming outbreaks of ZIKV and other arboviruses.

scholarly journals Caveats on COVID-19 herd immunity threshold: the Spain case

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
David García-García ◽  
Enrique Morales ◽  
Eva S. Fonfría ◽  
Isabel Vigo ◽  
Cesar Bordehore
Keyword(s):  
Upper Bound ◽  
Generation Time ◽  
Time Distribution ◽  
Herd Immunity ◽  
Late Summer ◽  
Spanish Population ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Population Estimates ◽  
Parameter Measuring

AbstractAfter a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2020 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2020 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

GLOBAL PROPERTIES FOR A VIRUS DYNAMICS MODEL WITH LYTIC AND NON-LYTIC IMMUNE RESPONSES, AND NONLINEAR IMMUNE ATTACK RATES

2014 ◽  
Vol 22 (03) ◽  
pp. 449-462 ◽  
Author(s):  
CRUZ VARGAS-DE-LEÓN
Keyword(s):  
Immune Responses ◽  
Viral Infection ◽  
Attack Rate ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Immune Effector ◽  
Global Properties ◽  
Immune Attack ◽  
The Stability ◽  
Stability Results

We consider a mathematical model that describes a viral infection with lytic and non-lytic immune responses. One of the main features of the model is that it includes a rate of linear activation of cytotoxic T lymphocytes (CTLs) immune response, a constant production rate of CTLs export from thymus, and a nonlinear attack rate for each immune effector mechanism. Stability of the infection-free equilibrium, and existence, uniqueness and stability of an immune-controlled equilibrium, are investigated. The stability results are given in terms of the basic reproductive number. We use the method of Lyapunov functions to study the global stability of the infection-free equilibrium and the immune-controlled equilibrium. We give a sufficient condition on the non-lytic-immune attack rate for the global asymptotic stability of the immune-controlled equilibrium. By theoretical analysis and numerical simulations, we show that the lytic and non-lytic activities are required to combat a viral infection.

scholarly journals Estimating the risk on outbreak spreading of 2019-nCoV in China using transportation data

2020 ◽  
Author(s):  
Hsiang-Yu Yuan ◽  
M. Pear Hossain ◽  
Mesfin Tsegaye ◽  
Xiaolin Zhu ◽  
Pengfei Jia ◽  
...  
Keyword(s):  
Arrival Time ◽  
Critical Time ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Framework ◽  
Cumulative Number ◽  
Border Control ◽  
Imported Cases ◽  
Novel Virus

AbstractA novel corona virus (2019-nCoV) was identified in Wuhan, China and has been causing an unprecedented outbreak in China. The spread of this novel virus can eventually become an international emergency. During the early outbreak phase in Wuhan, one of the most important public health tasks is to prevent the spread of the virus to other cities. Therefore, full-scale border control measures to prevent the spread of virus have been discussed in many nearby countries. At the same time, lockdown in Wuhan cityu (border control from leaving out) has been imposed. The challenge is that many people have traveled from Wuhan to other cities before the border control. Thus, it is difficult to forecast the number of imported cases at different cities and estimate their risk on outbreak emergence.Here, we have developed a mathematical framework incorporating city-to-city connections to calculate the number of imported cases of the novel virus from an outbreak source, and the cumulative number of secondary cases generated by the imported cases. We used this number to estimate the arrival time of outbreak emergence using air travel frequency data from Wuhan to other cities, collected from the International Air Transport Association database. In addition, a meta-population compartmental model was built based on a classical SIR approach to simulate outbreaks at different cities.We consider the scenarios under three basic reproductive number (R0) settings using the best knowledge of the current findings, from high (2.92), mild (1.68), to a much lower numbers (1.4). The mean arrival time of outbreak spreading has been determined. Under the high R0, the critical time is 17.9 days after December 31, 2019 for outbreak spreading. Under the low R0, the critical time is between day 26.2 to day 35 after December 31, 2019. To make an extra 30 days gain, under the low R0 (1.4), the control measures have to reduce 87% of the connections between the source and target cities. Under the higher R0 (2.92), the effect on reducing the chance of outbreak emergence is generally low until the border control measure was enhanced to reduce more than 95% of the connections.

scholarly journals An artificially simulated outbreak of a respiratory infectious disease

2019 ◽  
Author(s):  
Zuiyuan Guo ◽  
Shuang Xu ◽  
Libo Tong ◽  
Botao Dai ◽  
Yuandong Liu
Keyword(s):  
Infectious Disease ◽  
Infectious Diseases ◽  
Attack Rate ◽  
General Pattern ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Developmental Trend ◽  
Collision Model ◽  
Military Camp ◽  
Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often take place in crowded places. To understand the spreading pattern of an outbreak of a respiratory infectious disease and provide a theoretical basis for the targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between the onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeds 1.5, the median attack rate increases sharply; when R 0 =3, with a delay in the TOI, the attack rate increases gradually and eventually remains stable. If the IOI exceeds 2.3 days, the median attack rate will also increase dramatically. If the IR exceeds 0.5, the median of the attack rate nears zero. The median generation time was 8.26 days (95% CI: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and the R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusion The random collision model not only simulates how an epidemic spreads with superior precision but also allows more flexibility in the settings of the exposure population’s activities and different types of infectious diseases, which is conducive to furthering the exploration of the epidemiological characteristics of epidemic outbreaks.

scholarly journals The unexpected dynamics of COVID-19 in Manaus, Brazil: Herd immunity versus interventions

2021 ◽  
Author(s):  
Daihai He ◽  
Yael Artzy-Randrup ◽  
Salihu S. Musa ◽  
Lewi Stone
Keyword(s):  
Mathematical Modelling ◽  
Attack Rate ◽  
Herd Immunity ◽  
Indigenous Communities ◽  
Reproductive Number ◽  
Mortality Data ◽  
The World ◽  
The Media ◽  
The City ◽  
Second Wave

AbstractThe arrival of SARS-COV-2 in late March 2020 in the state of Amazonas, Brazil, captured worldwide attention and concern. The rapid growth of the epidemic, a health system that had collapsed, and mass gravesites for coping with growing numbers of dead, were broadcast by the media around the world. Moreover, a majority of the local Amazonian indigenous communities were physically distant from appropriate medical services, to the point where warnings of genocide were issued. In a recent Science paper (December 2020), Buss et al. reported that some 76% of the residents of the city of Manaus, the capital of Amazonas, had been infected by October 2020. This estimate of the COVID-19 attack rate was based on a seroprevalence analysis of blood donor data, which despite its shortcomings was thought to be a sufficiently reliable proxy of the larger population. An attack rate of this magnitude (76%) implied that herd immunity had already been reached and the community was relatively protected from further infection. Yet in December 2020, a harsh second wave of COVID-19 struck Manaus, and currently appears to be even larger than the first wave. Here we use mathematical modelling of mortality data in Manaus, and in various states of Brazil, to understand why a second wave appeared against all expectations. Our analysis is based on estimating a “flexible” reproductive number R0(t) from the mortality data, as it changes in time over the epidemic.

scholarly journals Estimating the reproductive number R0 of SARS-CoV-2 in the United States and eight European countries and implications for vaccination

2020 ◽  
Author(s):  
Ruian Ke ◽  
Ethan Obie Romero-Severson ◽  
Steven Sanche ◽  
Nick Hengartner
Keyword(s):  
United States ◽  
Herd Immunity ◽  
The United States ◽  
Control Measures ◽  
European Countries ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Individual Level ◽  
Epidemic Period ◽  
Induced Immunity

SARS-CoV-2 rapidly spread from a regional outbreak to a global pandemic in just a few months. Global research efforts have focused on developing effective vaccines against SARS-CoV-2 and the disease it causes, COVID-19. However, some of the basic epidemiological parameters, such as the exponential epidemic growth rate and the basic reproductive number, R0, across geographic areas are still not well quantified. Here, we developed and fit a mathematical model to case and death count data collected from the United States and eight European countries during the early epidemic period before broad control measures were implemented. Results show that the early epidemic grew exponentially at rates between 0.19-0.29/day (epidemic doubling times between 2.4-3.6 days). We discuss the current estimates of the mean serial interval, and argue that existing evidence suggests that the interval is between 6-8 days in the absence of active isolation efforts. Using parameters consistent with this range, we estimated the median R0 value to be 5.8 (confidence interval: 4.7-7.3) in the United States and between 3.6 and 6.1 in the eight European countries. This translates to herd immunity thresholds needed to stop transmission to be between 73% and 84%. We further analyze how vaccination schedules depends on R0, the duration of vaccine-induced immunity to SARS-CoV-2, and show that individual-level heterogeneity in vaccine induced immunity can significantly affect vaccination schedules.

scholarly journals COVID-19 PANDEMICS: HOW FAR ARE WE FROM HERD IMMUNITY?

2020 ◽  
Author(s):  
Carlos Hernandez-Suarez ◽  
Efren Murillo-Zamora ◽  
Francisco Espinoza Gómez
Keyword(s):  
Infection Rate ◽  
Study Design ◽  
Removal Rate ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Fatality Risk

ABSTRACTObjectivesto estimate the current number of total infections in a region in order to measure the progress of the epidemic with the purpose of reopening activities and planning the deployment of vaccines.Study designWe recovered estimates of the basic reproductive number (R0) and the Infection Fatality Risk (IFR) as well as the number of confirmed cases and deaths in several countries.Methodsthis works presents an expression to estimate the number of remaining susceptible in a population using the observed number of SARS-CoV-2 related deaths and current estimates of R0 and IFR.Resultsthe epidemic will infect most of the population causing 2.5 deaths per thousand inhabitants on average, and herd immunity will be achieved when the number of deaths per thousand inhabitants is close to two. This work introduces an expression to provide estimates of the number of remaining susceptible in a region using the reported number of deaths.Conclusionsany region with fewer than 2.5 deaths per thousand individuals will continue accumulating deaths until this average is achieved, and the infection rate will exceed the removal rate until the number of deaths is about two deaths per thousand, when herd immunity is reached. Waves may occur in any region where the number of deaths is below the herd immunity level.

scholarly journals Implications of Test Characteristics and Population Seroprevalence on “Immune Passport” Strategies

2020 ◽  
Author(s):  
Daniel B Larremore ◽  
Kate M Bubar ◽  
Yonatan H Grad
Keyword(s):  
False Positive ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Serological Tests ◽  
Test Characteristics ◽  
Simple Question ◽  
Minimum Requirements ◽  
Test Specificity ◽  
Repeat Infection

Abstract Various forms of “immune passports” or “antibody certificates” are being considered in conversations around reopening economies after periods of social distancing. A critique of such programs focuses on the uncertainty around whether seropositivity means immunity from repeat infection. However, an additional important consideration is that the low positive predictive value of serological tests in the setting of low population seroprevalence and imperfect test specificity will lead to many false-positive passport holders. Here, we pose a simple question: how many false-positive passports could be issued while maintaining herd immunity in the workforce? Answering this question leads to a simple mathematical formula for the minimum requirements of serological tests for a passport program, which depend on the population prevalence and the value of the basic reproductive number, R0. Our work replaces speculation in the press with rigorous analysis, and will need to be considered in policy decisions that are based on individual and population serology results.

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