Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number

Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R 0 , provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R 0 for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R 0 were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R 0 . The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate.

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Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

Scientific Reports ◽

10.1038/s41598-021-95913-8 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Md Abdul Kuddus ◽

M. Mohiuddin ◽

Azizur Rahman

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Transmission Rate ◽

Equilibrium Points ◽

Rank Correlation ◽

Dynamical Analysis ◽

Model Parameters ◽

Progression Rate ◽

Double Dose ◽

The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

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Modeling Transmission Dynamics ofStreptococcus suiswith Stage Structure and Sensitivity Analysis

Discrete Dynamics in Nature and Society ◽

10.1155/2014/432602 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10

Author(s):

Chaojian Shen ◽

Mingtao Li ◽

Wei Zhang ◽

Ying Yi ◽

Youming Wang ◽

...

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Stage Structure ◽

Sensitivity Analyses ◽

Effective Control ◽

Model Parameters ◽

Global Dynamics ◽

Deterministic Dynamic ◽

Globally Stable ◽

The Basic Reproduction Number

Streptococcosis is one of the major infectious and contagious bacterial diseases for swine farm in southern China. The influence of various control measures on the outbreaks and transmission ofS. suisis not currently known. In this study, in order to explore effective control and prevention measures we studied a deterministic dynamic model with stage structure forS. suis. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows that ifℛ0<1, the disease-free equilibrium is globally stable and the disease dies out, whereas ifℛ0>1, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. The model simulations well agree with new clinical cases and the basic reproduction number of this model is about 1.1333. Some sensitivity analyses ofℛ0in terms of the model parameters are given. Our study demonstrates that combination of vaccination and disinfection of the environment are the useful control strategy forS. suis.

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Uncertainty and Sensitivity Analysis of the In-Vessel Hydrogen Generation for Gen-III PWR and Phebus FPT-1 with MELCOR 2.2

Energies ◽

10.3390/en14164884 ◽

2021 ◽

Vol 14 (16) ◽

pp. 4884

Author(s):

Piotr Darnowski ◽

Piotr Mazgaj ◽

Mateusz Włostowski

Keyword(s):

Sensitivity Analysis ◽

Hydrogen Generation ◽

Rank Correlation ◽

Correlation Coefficients ◽

Latin Hypercube Sampling ◽

Severe Accident ◽

Sensitivity Analyses ◽

Pressurized Water ◽

Water Reactor ◽

Best Estimate

In this study, uncertainty and sensitivity analyses were performed with MELCOR 2.2.18 to study the hydrogen generation (figure-of-merit (FoM)) during the in-vessel phase of a severe accident in a light water reactor. The focus of this work was laid on a large generation-III pressurized water reactor (PWR) and a double-ended hot leg (HL) large break loss of coolant accident (LB-LOCA) without a safety injection (SI). The FPT-1 Phebus integral experiment emulating LOCA was studied, where the experiment outcomes were applied for the plant scale modelling. The best estimate calculations were supplemented with an uncertainty analysis (UA) based on 400 input-decks and Latin hypercube sampling (LHS). Additionally, the sensitivity analysis (SA) utilizing the linear regression and linear and rank correlation coefficients was performed. The study was prepared with a new open-source MELCOR sensitivity and uncertainty tool (MelSUA), which was supplemented with this work. The FPT-1 best-estimate model results were within the 10% experimental uncertainty band for the final FoM. It was shown that the hydrogen generation uncertainties in PWR were similar to the FPT-1, with the 95% percentile being covered inside a ~50% band and the 50% percentile inside a ~25% band around the FoM median. Two different power profiles for PWR were compared, indicating its impact on the uncertainty but also on the sensitivity results. Despite a similar setup, different uncertainty parameters impacted FoM, showing the difference between scales but also a significant impact of boundary conditions on the sensitivity analysis.

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

10.21203/rs.3.rs-257453/v1 ◽

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).

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Epidemic model formulation and analysis for diarrheal infections caused by salmonella

SIMULATION ◽

10.1177/0037549716685409 ◽

2017 ◽

Vol 93 (7) ◽

pp. 543-552 ◽

Cited By ~ 1

Author(s):

Ojaswita Chaturvedi ◽

Mandu Jeffrey ◽

Edward Lungu ◽

Shedden Masupe

Keyword(s):

Parameter Estimation ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Elementary Model ◽

Partial Rank Correlation ◽

Parameter Values ◽

Working Out ◽

Disease Free

Epidemic modeling can be used to gain better understanding of infectious diseases, such as diarrhea. In the presented research, a continuous mathematical model has been formulated for diarrhea caused by salmonella. This model has been analyzed and simulated to be established in a functioning form. Elementary model analysis, such as working out the disease-free state and basic reproduction number, has been done for this model. The basic reproduction number has been calculated using the next generation matrix method. Stability analysis of the model has been done using the Routh–Hurwitz method. Sensitivity analysis and parameter estimation have been completed for the system too using MATLAB packages that work on the Latin Hypercube Sampling and Partial Rank Correlation Coefficient methods. It was established that as long as R0 < 1, there will be no epidemic. Upon simulation using assumed parameter values, the results produced comprehended the epidemic theory and practical situations. The system was proven stable using the Routh–Hurwitz criterion and parameter estimation was successfully completed. Salmonella diarrhea has been successfully modeled and analyzed in this research. This model has been flexibly built and it can be integrated onto certain platforms to be used as a predictive system to prevent further infections of salmonella diarrhea.

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Uncertainty and sensitivity analysis of the basic reproduction number of diphtheria: a case study of a Rohingya refugee camp in Bangladesh, November–December 2017

PeerJ ◽

10.7717/peerj.4583 ◽

2018 ◽

Vol 6 ◽

pp. e4583 ◽

Cited By ~ 12

Author(s):

Ryota Matsuyama ◽

Andrei R. Akhmetzhanov ◽

Akira Endo ◽

Hyojung Lee ◽

Takayuki Yamaguchi ◽

...

Keyword(s):

Sensitivity Analysis ◽

Basic Reproduction Number ◽

Process Model ◽

Large Scale ◽

Reproduction Number ◽

Latin Hypercube Sampling ◽

Refugee Camp ◽

Background Information ◽

The Basic Reproduction Number

BackgroundA Rohingya refugee camp in Cox’s Bazar, Bangladesh experienced a large-scale diphtheria epidemic in 2017. The background information of previously immune fraction among refugees cannot be explicitly estimated, and thus we conducted an uncertainty analysis of the basic reproduction number,R0.MethodsA renewal process model was devised to estimate theR0and ascertainment rate of cases, and loss of susceptible individuals was modeled as one minus the sum of initially immune fraction and the fraction naturally infected during the epidemic. To account for the uncertainty of initially immune fraction, we employed a Latin Hypercube sampling (LHS) method.ResultsR0ranged from 4.7 to 14.8 with the median estimate at 7.2.R0was positively correlated with ascertainment rates. Sensitivity analysis indicated thatR0would become smaller with greater variance of the generation time.DiscussionEstimatedR0was broadly consistent with published estimate from endemic data, indicating that the vaccination coverage of 86% has to be satisfied to prevent the epidemic by means of mass vaccination. LHS was particularly useful in the setting of a refugee camp in which the background health status is poorly quantified.

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Could Condoms Stop the AIDS Epidemic?

Journal of Theoretical Medicine ◽

10.1080/10273660412331315147 ◽

2003 ◽

Vol 5 (3-4) ◽

pp. 171-181 ◽

Cited By ~ 21

Author(s):

Seyed M. Moghadas ◽

Abba B. Gumel ◽

Robert G. McLeod ◽

Richard Gordon

Keyword(s):

Meta Analysis ◽

Treatment Strategies ◽

Rank Correlation ◽

Correlation Coefficients ◽

Latin Hypercube Sampling ◽

Sensitivity Analyses ◽

Parameter Estimates ◽

Current Estimate ◽

Aids Epidemic ◽

Hiv Aids

Although therapeutic treatment strategies appear promising for retarding the progression of HIV-related diseases, prevention remains the most effective strategy against the HIV/AIDS epidemic. This paper focuses on the effect of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. There are two primary factors in the use of condoms to halt the HIV/AIDS epidemic: condom efficacy and compliance. Our study is focused on the effect of these factors in stopping the epidemic by constructing a new deterministic mathematical model. The current estimate of condom effectiveness against HIV transmission, based on the latest meta-analysis, is 60–96%, with a mean of 87%. Since the parameter estimates are subject to different kinds of uncertainty, to achieve adequate quality assurance in predictions, uncertainty and sensitivity analyses are carried out using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs). Using stability and sensitivity analyses, based on a plausible range of parameter values, key parameters that govern the persistence or eradication of HIV are identified. This analysis shows that the product of efficacy and compliance, which we call ‘preventability’ (p), has a negative effect on the epidemic; as increasingpdecreases the level of epidemicity. It is also shown that the threshold preventability (pc) increases with increasing average number of HIV-infected partners of susceptible individuals, especially those in the AIDS stage. For populations where the average number of HIV-infected partners is large, the associated preventability threshold is high and perhaps unattainable, suggesting that for such a population, HIV may not be controlled using condoms alone. On the other hand, for a population where the average number of HIV-infected partners is low (within a reasonable range), it is shown thatpcis about 75%, suggesting that the epidemic could be stopped using condoms. Thus, for such a population, public health measures that can bring preventability above the threshold and continuous quantitative monitoring to make sure it stays there, are what would be necessary. In other words, for populations with reasonable average numbers of HIV-infected partners, given the will and effort, it is within our means to halt this epidemic using condoms.

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Variants of SARS-COV-2 and the Death Toll

10.1101/2021.07.08.21260081 ◽

2021 ◽

Author(s):

Takesi Saito

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Death Toll ◽

The Uk ◽

Spread Of Infection ◽

The Basic Reproduction Number

New variants of SARS-COV-2 have been found in various countries. Especially, the UK has been attacked by India's Delta Plus, and the spread of infection has been very rapid, since it is extremely infectious. Fortunately, however, the number of deaths has been stayed flat, where deaths are reported to be those who are not yet received a shot of COVID-19 vaccine. In this note, we would like to consider why the number of deaths is so small, compared with high cases, around the infection peak, when the basic reproduction number is very large.

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Using the basic reproduction number to assess the risk of transmission of lumpy skin disease virus by biting insects

10.1101/602292 ◽

2019 ◽

Author(s):

Simon Gubbins

Keyword(s):

Disease Virus ◽

Basic Reproduction Number ◽

Skin Disease ◽

Reproduction Number ◽

Sensitivity Analyses ◽

Published Data ◽

Mechanical Transmission ◽

Lumpy Skin Disease ◽

Lumpy Skin Disease Virus ◽

The Basic Reproduction Number

SummaryIn recent years, lumpy skin disease virus (LSDV) has emerged as a major threat to cattle outside Africa, where it is endemic. Although evidence suggests that LSDV is transmitted by the bites of blood sucking arthropods, few studies have assessed the risk of transmission posed by particular vector species. Here this risk is assessed by calculating the basic reproduction number (R0) for transmission of LSDV by five species of biting insect: the stable fly, Stomoxys calcitrans, the biting midge, Culicoides nubeculosus, and three mosquito species, Aedes aegypti, Anopheles stephensi and Culex quinquefasciatus. Parameters relating to mechanical transmission of LSDV were estimated using new analyses of previously-published data from transmission experiments, while vector life history parameters were derived from the published literature. Uncertainty and sensitivity analyses were used to compute R0 for each species and to identify those parameters which influence its magnitude. Results suggest that S. calcitrans is likely to be the most efficient at transmitting LSDV, with Ae. aegypti also an efficient vector. By contrast, C. nubeculosus, An. stephensi, and Cx. quinquefasciatus are likely to be inefficient vectors of LSDV. However, there is considerable uncertainty associated with the estimates of R0, reflecting uncertainty in most of the constituent parameters. Sensitivity analysis suggests that future experimental work should focus on estimating the probability of transmission from insect to bovine and on the virus inactivation rate in insects.

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Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea

Computational and Mathematical Methods in Medicine ◽

10.1155/2015/582625 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 4

Author(s):

Zhiming Li ◽

Zhidong Teng ◽

Xiaomei Feng ◽

Yingke Li ◽

Huiguo Zhang

Keyword(s):

Basic Reproduction Number ◽

Epidemic Model ◽

Ebola Virus ◽

Reproduction Number ◽

Rank Correlation ◽

Least Square Method ◽

Least Square ◽

Dynamical Analysis ◽

Infectious Individual ◽

The Basic Reproduction Number

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the model by the least square method. With suitable parameter values, we obtain the estimated value of the basic reproduction number and analyze the sensitivity and uncertainty property by partial rank correlation coefficients.

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