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At least 19 recordsLinked to original sources
PubMed1999

The basic reproduction number for scrapie.

The basic reproduction number R0 provides a quantitative assessment of the ability of an infectious agent to invade a susceptible host population. A mathematical expression for R0 is derived based on a recently developed model for the spread of scrapie through a flock of sheep. The model incorporates sheep demography, a long and variable incubation period, genetic variation in susceptibility to scrapie, and horizontal and vertical routes of transmission. The sensitivity of R0 to a range of epidemiologically important parameters is assessed and the effects of genetic variation in susceptibility are examined. A reduction in the frequency of the susceptibility allele reduces R0 most effectively when the allele is recessive, whereas inbreeding may increase R0 when the allele is recessive, increasing the chance of an outbreak. Using this formulation, R0 is calculated for an outbreak of scrapie in a flock of Cheviot sheep.

Animals↗
PubMed1993

The estimation of the basic reproduction number for infectious diseases.

The basic reproduction number R0 is the number of secondary cases which one case would produce in a completely susceptible population. It depends on the duration of the infectious period, the probability of infecting a susceptible individual during one contact, and the number of new susceptible individuals contacted per unit of time. Therefore R0 may vary considerably for different infectious diseases but also for the same disease in different populations. The key threshold result of epidemic theory associates the outbreaks of epidemics and the persistence of endemic levels with basic reproduction numbers greater than one. Because the magnitude of R0 allows one to determine the amount of effort which is necessary either to prevent an epidemic or to eliminate an infection from a population, it is crucial to estimate R0 for a given disease in a particular population. The present paper gives a survey about the various estimation methods available.

Acquired Immunodeficiency Syndrome↗
PubMed1996

On estimating the basic reproduction number for Schistosoma haematobium.

Existing estimates of the basic reproduction number, Ro, for human schistosomes are mostly in the range 1-4, implying that schistosomes should be relatively easy to eliminate from endemic areas, which is contrary to practical experience. An estimate of Ro for a site in Zimbabwe is obtained here using a mathematical model explicitly incorporating two features believed to be epidemiologically significant; age-dependent exposure and acquired immunity. Parameter estimates are, as far as possible, obtained independently, but the coefficients representing man-snail and snail-man transmission, as well as parameters representing effects of acquired immunity, must be estimated indirectly by fitting the model to field data. Heterogeneity in human exposure and contamination is crudely incorporated by considering "wormy' and non-wormy' fractions of the population. The results suggest Ro to be in the range 4-5 or more, higher than previous estimates and despite only moderate levels of infection at this site. It is shown that this estimate is sensitive to the form of the underlying model. The application of less realistic models may lead to less reliable estimates of Ro.

Animals↗
PubMed1996

Vector-borne diseases and the basic reproduction number: a case study of African horse sickness.

The basic reproduction number, R0, can be used to determine factors important in the ability of a disease to invade or persist. We show how this number can be derived or estimated for vector-borne diseases with different complicating factors. African horse sickness is a viral disease transmitted mainly by the midge Culicoides imicola. We use this as an example of such a vector-transmitted disease where latent periods, seasonality in vector populations, and multiple host types may be important. The effect of vector population dynamics which are dependent on either host or vector density are also addressed. If density-dependent constraints on vector population density are less severe, R0 is more sensitive to vector mortality and the virus development rate. Host-dependent vector dynamics change the relationship between R0 and host population size. Seasonality can either increase or decrease the estimate of R0, depending on the lag between the peak of the midge population and the infective host population. The relative abundance of two host types is a factor in the ability of a disease to invade, but the strength of this factor depends on the differences between the hosts in recovery from infection, mortality and transmission. Removal of a reservoir host may increase R0.

African Horse Sickness↗
PubMed2006

Basic reproduction number for HIV model incorporating commercial sex and behavior change.

The basic reproduction number is obtained for an HIV epidemic model incorporating direct and indirect commercial sex as well as behavior change by the female commercial sex workers (CSWs) and their male customers in response to the proliferation of the disease in the community. A recent result by van den Driessche P., and Watmough J. (Math. Biosci. 180:29-48, 2002) is utilized to compute the threshold parameters for the local asymptotic stability of the Disease-Free Equilibrium (DFE), by considering the transfers in and out of the infective classes. Numerical examples are used to describe the uniqueness and global properties of the endemic equilibrium when DFE is unstable. Biological interpretation of the results obtained in this work is discussed, as are the implications of our results for the design of public health policies such as targeting strategy to target intervention and control measures toward specific high-risk population groups in order to reduce infections. We show that targeting any one sector of the commercial sex alone for prevention will be difficult to have a decided effect on eradicating the epidemic. However, if the aim of the targeted intervention policy is not eradication of the epidemic but decrease in HIV incidence of a particular high-risk group, then concentrated targeting strategy could be sufficient, if properly implemented. This work also demonstrates the usefulness of the theorem of van den Driessche and Watmough (Math. Biosci. 180:29-48, 2002) in obtaining threshold parameters for complicated infectious diseases models.

Algorithms↗
PubMed1999

Estimation of the basic reproduction number of BSE: the intensity of transmission in British cattle.

The basic reproduction number, R0, of an infectious agent is a key factor determining the rate of spread and the proportion of the host population affected. We formulate a general mathematical framework to describe the transmission dynamics of long incubation period diseases with complex pathogenesis. This is used to derive expressions for R0 of bovine spongiform encephalopathy (BSE) in British cattle, and back-calculation methods are used to estimate R0 throughout the time-course of the BSE epidemic. We show that the 1988 meat and bonemeal ban was effective in rapidly reducing R0 below 1, and demonstrate that this indicates that BSE will be unable to become endemic in the UK cattle population even when case clustering is taken into account. The analysis provides some insight into absolute infectiousness for bovine-to-bovine transmission, indicating maximally infectious animals may have infected up to 400 animals each. The relationship between R0 and the early stages of the BSE epidemic and the requirements for additional research are also discussed.

Animal Feed↗
PubMed1992

Mathematical modelling and theory for estimating the basic reproduction number of canine leishmaniasis.

The paper describes a mathematical model for canine leishmaniasis and presents formulae which can be used to estimate the basic reproduction number, R0. The primary concern has been to devise methods of estimation which make best use of those data most easily obtained by fieldwork, e.g. surveys of prevalence in dog (by age) and sandfly populations. A range of formulae are offered which are more or less demanding of data, and which consequently give more or less precise estimates of R0. They include methods for assessing the influence on R0 of heterogeneous biting rates of sandflies on dogs, in which the essence of heterogeneous transmission can be captured merely by measuring relative rather than absolute contact rates.

Animals↗
PubMed1999

Some properties of an estimator for the basic reproduction number of the general epidemic model.

In this paper some properties of a convenient estimator, derived from a martingale estimating function, for the basic reproduction number of the general epidemic model are given for both finite and large samples. These properties give some guidelines for using this convenient estimator. It is shown that it underestimates the parameter and that the bias tends to zero when the population size and the initial number of infectives are increased simultaneously. The bias cannot be removed for a fixed number of introductory infectives. However, the estimator is asymptotically unbiased, conditional on a major outbreak. A simulation study shows that the central limit theorem applies for moderate population sizes.

Bias↗
PubMed2005

The basic reproductive number of tick-borne encephalitis virus. An empirical approach.

Tick-borne encephalitis virus (TBEV) is reciprocally transmitted between Ixodes ricinus ticks and small mammals. Recently, transmission between co-feeding ticks has been postulated as an epidemiological by important mechanism of perpetuating the agent. To empirically examine the question whether the "traditional" mode of transmission is sufficient to maintain enzootic TBEV transmission, the basic reproductive number R(0) of TBEV could be estimated under this model for sites in which TBEV is enzootic. I propose an empirical estimator of R(0) for TBEV which is based on longitudinal stage-specific local tick infestation densities assessed by live trapping of small mammals. A Gibbs sampler-based 95%-credibility interval is presented. When applied to published field data from TBEV enzootic sites sub-critical R(0) estimates are obtained for both sites. I discuss potential shortcomings of this method and possible implications of these findings on the discussion of supplemental mechanisms of transmission.

Animals↗
PubMed2001

Basic reproduction number for the transmission of Plasmodium vivax malaria.

The possibility of relapse is introduced into a mathematical model for the transmission of Plasmodium vivax malaria. In the model, the human population is divided into four classes: susceptible, infected, dormant and recovered. Loss of immunity by individuals in the recovered class moves these individuals back into the susceptible class. Two equilibrium states are found, a disease-free state and an endemic state. A basic reproduction number Ro is found. Depending on whether Ro is less than or greater than one. the disease free state or the endemic state results. The dependence of Ro on the rate of relapse is determined and the implication of this dependence is identified.

Animals↗
PubMed2000

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

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%.

Adult↗
PubMed2000

Estimation of a time-varying force of infection and basic reproduction number with application to an outbreak of classical swine fever.

BACKGROUND: A method was developed for stochastically reconstructing the pattern of infection from observed epidemic data. This allowed for estimation of a time-dependent force of infection, or transmission rate, during an epidemic. METHODS: A discrete-time mechanistic model was used to describe the spread of infection and a stochastic procedure, which utilised the latent and infectious period distributions, was used to reconstruct the dates of infection, becoming infectious and removal from the given data. The four equations describing the model were then solved to obtain least squares estimates of the transmission rate and the basic reproduction number (R0) throughout the epidemic. This process was repeated in order to assess the variability in these key epidemiological parameters. The stochastic epidemic reconstruction procedure was developed to account for changes in the distribution of the survival period over the course of the epidemic and adapted for application to epidemic data where not all infected individuals have yet been observed as cases. RESULTS: The method was applied to a set of epidemic data from an outbreak of classical swine fever in Pakistan. Constant and time-varying estimates of the transmission rate were derived and compared. There was some evidence to suggest that the force of infection varied over time. DISCUSSION: The method described can be applied to data from epidemics where observations are incomplete. The confidence limits obtained for the estimated force of infection provide a means of assessing the evidence for time variation in this parameter.

Animals↗
PubMed2004

The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda.

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.

Congo↗
PubMed1992

Epidemiology of canine leishmaniasis: prevalence, incidence and basic reproduction number calculated from a cross-sectional serological survey on the island of Gozo, Malta.

Assessment of the resilience of canine leishmaniasis to control or, more ambitiously, the effort needed to eradicate infection, requires an estimate of the basic case reproduction number (R0). This paper applies the theoretical results of Hasibeder, Dye & Carpenter (1992) to data from a cross-sectional survey on the Maltese island of Gozo in which dogs of known age, sex and occupation (pet, guard etc) were subjected to three different serological tests for the presence of specific antibody (IFAT, DAT and ELISA). Difficulties in interpreting these test results, and hence of determining the proportion of dogs infected, present the main obstacle to estimating R0: estimates are critically dependent on the choice of threshold separating seropositives from seronegatives. The data do, however, allow a robust comparative analysis of risk which shows that the force of infection experienced by working dogs is about three times higher than that of pet dogs, a degree of non-homogeneous contact which actually has little effect on estimates of R0. We suggest a cautious point estimate of R0 congruent to 11, and comment briefly on its significance for leishmaniasis control.

Age Factors↗
PubMed1998

The long-term dynamics of tuberculosis and other diseases with long serial intervals: implications of and for changing reproduction numbers.

The net and basic reproduction numbers are among the most widely-applied concepts in infectious disease epidemiology. A net reproduction number (the average number of secondary infectious cases resulting from each case in a given population) of above 1 is conventionally associated with an increase in incidence; the basic reproduction number (defined analogously for a 'totally susceptible' population) provides a standard measure of the 'transmission potential' of an infection. Using a model of the epidemiology of tuberculosis in England and Wales since 1900, we demonstrate that these measures are difficult to apply if disease can follow reinfection, and that they lose their conventional interpretations if important epidemiological parameters, such as the rate of contact between individuals, change over the time interval between successive cases in a chain of transmission (the serial interval). The net reproduction number for tuberculosis in England and Wales appears to have been approximately 1 from 1900 until 1950, despite concurrent declines in morbidity and mortality rates, and it declined rapidly in the second half of this century. The basic reproduction number declined from about 3 in 1900, reached 2 by 1950, and first fell below 1 in about 1960. Reductions in effective contact between individuals over this period, measured in terms of the average number of individuals to whom each case could transmit the infection, meant that the conventional basic reproduction number measure (which does not consider subsequent changes in epidemiological parameters) for a given year failed to reflect the 'actual transmission potential' of the infection. This latter property is better described by a variant of the conventional measure which takes secular trends in contact into account. These results are relevant for the interpretation of trends in any infectious disease for which epidemiological parameters change over time periods comparable to the infectious period, incubation period or serial interval.

Adolescent↗
PubMed2006

The minimum effort required to eradicate infections in models with backward bifurcation.

We study an epidemiological model which assumes that the susceptibility after a primary infection is r times the susceptibility before a primary infection. For r = 0 (r = 1) this is the SIR (SIS) model. For r > 1 + (mu/alpha) this model shows backward bifurcations, where mu is the death rate and alpha is the recovery rate. We show for the first time that for such models we can give an expression for the minimum effort required to eradicate the infection if we concentrate on control measures affecting the transmission rate constant beta. This eradication effort is explicitly expressed in terms of alpha,r, and mu As in models without backward bifurcation it can be interpreted as a reproduction number, but not necessarily as the basic reproduction number. We define the relevant reproduction numbers for this purpose. The eradication effort can be estimated from the endemic steady state. The classical basic reproduction number R0 is smaller than the eradication effort for r > 1 + (mu/alpha) and equal to the effort for other values of r. The method we present is relevant to the whole class of compartmental models with backward bifurcation.

Algorithms↗