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Results for “Basic Reproduction Number”

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At least 145 records · Page 8Linked to original sources

PubMed2002

Comparison of vaccination strategies for the control of dog rabies in Machakos District, Kenya.

Demographic and epidemiological field data were used in a deterministic model to describe dog rabies transmission in Machakos District, Kenya and to predict the impact of potential vaccination strategies for its control. The basic reproduction number (R0) was estimated to be 2.44 (1.52-3.36, 95% confidence limits). There were three key model predictions. The first was that a threshold dog density (K(T)) of 4.5 dogs km(-2) (3.8-5.2 dogs km(-2), 95% confidence limits) was required to maintain transmission. The second was that the estimated annual vaccination rate of 24% failed to decrease incidence and actually increased the stability of transmission and may be counter-productive. Thirdly, to control rabies, it was predicted that 59% (34%-70%, 95% confidence limits) of dogs should be vaccinated at any one time. This requires approximately 70% coverage for annual but only 60% coverage for semi-annual vaccination campaigns. Community-level vaccination trials are needed to test these predictions.

Animals↗

PubMed2003

Dynamics of a scrapie outbreak in a flock of Romanov sheep--estimation of transmission parameters.

Knowledge of epidemiological mechanisms and parameters underlying scrapie transmission in sheep flocks remains very limited at present. Here we introduce a method for fitting stochastic transmission models to outbreak data to estimate bounds on key transmission parameters. We apply this method to data describing an outbreak of scrapie in a closed flock of Romanov sheep. The main findings are that the relative infectiousness of infected animals in this outbreak becomes appreciable early into disease incubation and that the mean incubation period is less than 1.5 years. We also find that the data are consistent with a broad range of values for the basic reproduction number R0 and describe how the boundaries of this range depend on assumptions about the mean incubation period and the contribution to transmission of a long-lived environmental reservoir of infectivity.

Animals↗

PubMed2004

Modelling responses to a smallpox epidemic taking into account uncertainty.

Epidemiology and modelling are currently under pressure to build consistent scenarios of control in case of deliberate release of biological weapons. In order to assess the key parameters for the control of a smallpox outbreak in a large city (2 million inhabitants), we built a stochastic model to simulate the course of an epidemic controlled by ring vaccination and case isolation. Assuming a reference scenario with 100 index cases and implementation of intervention 25 days after the attack, the model forecasts an epidemic of 730 cases with an epidemic duration of 240 days. Setting intervention 20 days later would result in an almost fourfold increase in the epidemic size. A multivariate sensitivity analysis has selected three key parameters: the basic reproduction number (i.e. the number of secondary cases infected by one case in an entirely susceptible population, equal to 3 in the reference scenario), time to intervention, and proportion of traced and vaccinated contacts.

Algorithms↗

PubMed2004

A scrapie epidemic in Cyprus.

Scrapie is endemic in the sheep flocks of many countries, but good epidemiological information on this disease is scarce. Data on the initial stages of an epidemic are even more rare. We describe the ongoing epidemic of scrapie in Cyprus that has been tracked since it began in the mid-1980s. The early stages of the spread of scrapie from farm to farm, between 1985 and 2000, is analysed with a simple mathematical model. The flock-to-flock basic reproductive number (R0) for the spread of scrapie was estimated at between 1.4 and 1.8. The impact of interventions on the control of the epidemic are discussed from an epidemiological and economic point of view. Early identification of scrapie cases on farms can have a large impact on the number of farms affected. The long period before detection of disease in a flock means that policies based on whole-flock slaughter can be inefficient in preventing spread. Under a range of scenarios, a concentration of resources on early detection and quarantine may be more effective in terms of both the costs and control of the epidemic.

Animals↗

PubMed2005

Modelling and determination of the transmission contact rate for contagious bovine pleuropneumonia.

Contagious bovine pleuropneumonia (CBPP) is a cattle respiratory disease that represents one of the major threats to cattle health and production in sub-Saharan Africa. The transmission contact rate of CBPP plays a key role in the spreading dynamics of the disease. We have developed an approach based on the combination of a SEIR model describing the spread of CBPP with the dynamic of seroconversion to determine the transmission contact rate for CBPP. This method has been subsequently applied to serological diagnostic data obtained from an experimental vaccine trial. As a result, we find that the transmission contact rates for subclinical, clinical and chronic infective states are respectively, 0.084/N, 0.45 and 0.14/N per animal per day, where N is the herd population size, and the basic reproductive number corresponding to this trial (N=28) is R0=27.

Africa↗

PubMed2005

Matrix models for childhood infections: a Bayesian approach with applications to rubella and mumps.

Mathematical modelling is an established tool for planning and monitoring vaccination programmes. However, the matrices describing contact rates are based on subjective choices, which have a large impact on results. This paper reviews published models and obtains prior model probabilities based on publication frequency and expert opinion. Using serological survey data on rubella and mumps, Bayesian methods of model choice are applied to select the most plausible models. Estimates of the basic reproduction number R0 are derived, taking into account model uncertainty and individual heterogeneity in contact rates. Twenty-two models are documented, for which publication frequency and expert opinion are negatively correlated. Using the expert prior with individual heterogeneity, R0=6.1 [95% credible region (CR) 4.3-9.2] for rubella and R0=19.3 (95% CR 4.0-31.5) for mumps. The posterior modes are insensitive to the prior for rubella but not for mumps. Overall, assortative models with individual heterogeneity are recommended.

Bayes Theorem↗

PubMed2006

Understanding the dynamics of Ebola epidemics.

Ebola is a highly lethal virus, which has caused at least 14 confirmed outbreaks in Africa between 1976 and 2006. Using data from two epidemics [in Democratic Republic of Congo (DRC) in 1995 and in Uganda in 2000], we built a mathematical model for the spread of Ebola haemorrhagic fever epidemics taking into account transmission in different epidemiological settings. We estimated the basic reproduction number (R0) to be 2.7 (95% CI 1.9-2.8) for the 1995 epidemic in DRC, and 2.7 (95% CI 2.5-4.1) for the 2000 epidemic in Uganda. For each epidemic, we quantified transmission in different settings (illness in the community, hospitalization, and traditional burial) and simulated various epidemic scenarios to explore the impact of control interventions on a potential epidemic. A key parameter was the rapid institution of control measures. For both epidemic profiles identified, increasing hospitalization rate reduced the predicted epidemic size.

Africa, Central↗

PubMed2007

Comparison of smallpox outbreak control strategies using a spatial metapopulation model.

To determine the potential benefits of regionally targeted mass vaccination as an adjunct to other smallpox control strategies we employed a spatial metapopulation patch model based on the administrative districts of Great Britain. We counted deaths due to smallpox and to vaccination to identify strategies that minimized total deaths. Results confirm that case isolation, and the tracing, vaccination and observation of case contacts can be optimal for control but only for optimistic assumptions concerning, for example, the basic reproduction number for smallpox (R0=3) and smaller numbers of index cases ( approximately 10). For a wider range of scenarios, including larger numbers of index cases and higher reproduction numbers, the addition of mass vaccination targeted only to infected districts provided an appreciable benefit (5-80% fewer deaths depending on where the outbreak started with a trigger value of 1-10 isolated symptomatic individuals within a district).

Disease Outbreaks↗

PubMed1997

Transmission and distribution of virus serotypes: African horse sickness in zebra.

The prevalence of African horse sickness (AHS) serotypes in zebra foals from the Kruger National Park, South Africa was examined for possible associations between serotypes and to estimate the basic reproduction number, R0. The distributions of serotypes between zebra were not independent in the 6- and 7-8-month-old age classes (P < 0.005). This does not necessarily imply biological interactions between serotypes, as heterogeneity in host-vector transmission rates can generate non-independent distributions of serotypes. Both age and month of capture were significant factors in the number of serotypes infecting each zebra (P < 0.0001). Pairwise, positive associations between non-cross-reacting serotypes were found in the 7-8-month-old class only. For AHS overall, estimates of R0 ranged from 31-68. Assuming serotypes are transmitted independently, estimates of R0 for individual serotypes ranged from 10 for serotype 1 to 23 for serotype 6. The wide range of estimates emphasizes the need for a better understanding of serotype transmission and interactions in AHS.

African Horse Sickness↗

PubMed2004

Time-delay dynamics for contagious bovine pleuropneumonia.

Modelling of contagious disease usually employs compartmental SEIR-like models where the waiting times in respective compartments are exponentially distributed. In this paper, we are interested in investigating how the distributions of sojourn times in infective compartments affect the dynamics and persistence of the contagious bovine pleuropneumonia, a chronic respiratory disease of cattle. Two kinds of extreme distributions of the sojourn times are considered: a Dirac delta-function and truncated Gaussian function leading to a model with (non-constant) delay and the classical exponential distribution that stands for a model without delay. Expressions of the basic reproductive numbers are derived and dynamical behaviours are discussed for the three models. It is found that the spreading of disease exhibits wave-like oscillations for the time-delay dynamics. In contrast, the disease appears to last longer when the spreading is described by the classical dynamics without delay. Subsequently, the time-delay dynamics turns out to be more appropriate for the description of an experimental epidemic of CBPP.

Animals↗

PubMed1996

Allometry and simple epidemic models for microparasites.

Simple mathematical models for microparasites offer a useful way to examine the population dynamics of different viral and bacterial pathogens. One constraint in applying these models in free-living host populations is the paucity of data with which to estimate transmission rates. Here we recast a standard epidemiological model by setting the birth and death rates of the host population and its density as simple allometric functions of host body weight. We then use standard threshold theorems for the model in order to estimate the minimum rate of transmission for the parasite to establish itself in a mammalian host population. Transmission rates that produce different comparable values of the parasites' basic reproductive number, RO, are themselves allometric functions of host body size. We have extended the model to show that hosts having different body sizes suffer epidemic outbreaks whose frequency scales with body size. The expected epidemic periods for pathogens in different mammalian populations correspond to cycles observed in free-living populations.

Animals↗

PubMed2003

The role of evolution in the emergence of infectious diseases.

It is unclear when, where and how novel pathogens such as human immunodeficiency virus (HIV), monkeypox and severe acute respiratory syndrome (SARS) will cross the barriers that separate their natural reservoirs from human populations and ignite the epidemic spread of novel infectious diseases. New pathogens are believed to emerge from animal reservoirs when ecological changes increase the pathogen's opportunities to enter the human population and to generate subsequent human-to-human transmission. Effective human-to-human transmission requires that the pathogen's basic reproductive number, R(0), should exceed one, where R(0) is the average number of secondary infections arising from one infected individual in a completely susceptible population. However, an increase in R(0), even when insufficient to generate an epidemic, nonetheless increases the number of subsequently infected individuals. Here we show that, as a consequence of this, the probability of pathogen evolution to R(0) > 1 and subsequent disease emergence can increase markedly.

Animals↗

PubMed2005

Strategies for containing an emerging influenza pandemic in Southeast Asia.

Highly pathogenic H5N1 influenza A viruses are now endemic in avian populations in Southeast Asia, and human cases continue to accumulate. Although currently incapable of sustained human-to-human transmission, H5N1 represents a serious pandemic threat owing to the risk of a mutation or reassortment generating a virus with increased transmissibility. Identifying public health interventions that might be able to halt a pandemic in its earliest stages is therefore a priority. Here we use a simulation model of influenza transmission in Southeast Asia to evaluate the potential effectiveness of targeted mass prophylactic use of antiviral drugs as a containment strategy. Other interventions aimed at reducing population contact rates are also examined as reinforcements to an antiviral-based containment policy. We show that elimination of a nascent pandemic may be feasible using a combination of geographically targeted prophylaxis and social distancing measures, if the basic reproduction number of the new virus is below 1.8. We predict that a stockpile of 3 million courses of antiviral drugs should be sufficient for elimination. Policy effectiveness depends critically on how quickly clinical cases are diagnosed and the speed with which antiviral drugs can be distributed.

Age Distribution↗

PubMed2005

Superspreading and the effect of individual variation on disease emergence.

Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R(0), which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R(0) can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous 'superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R(0) is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.

Contact Tracing↗

PubMed2000

The importance of immediate destruction in epidemics of foot and mouth disease.

Foot and mouth disease is still prevalent in many parts of the world, as emphasised by the recent devastating epidemic in pig farms in Taiwan. A discrete time mechanistic model has been used to describe the spread of infection in both this epidemic and the 1967 to 1968 epidemic in the UK. The force of infection and basic reproduction number are estimated and the sensitivity of these results to the distributions of both the latent and infectious periods of the disease is examined. Epidemic simulations were performed to evaluate the disease control policy whereby all herds are slaughtered on the same day as disease confirmation. These simulations showed that implementing this policy could have resulted in a dramatic reduction (of over 60 per cent) in the number of pig farms affected in the Taiwan epidemic. It is thus imperative that the necessary resources are available to implement this policy, should an outbreak occur.

Animals↗

PubMed2005

Multiscale, resurgent epidemics in a hierarchical metapopulation model.

Although population structure has long been recognized as relevant to the spread of infectious disease, traditional mathematical models have understated the role of nonhomogenous mixing in populations with geographical and social structure. Recently, a wide variety of spatial and network models have been proposed that incorporate various aspects of interaction structure among individuals. However, these more complex models necessarily suffer from limited tractability, rendering general conclusions difficult to draw. In seeking a compromise between parsimony and realism, we introduce a class of metapopulation models in which we assume homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains. We model the movement of individuals between contexts via simple transport parameters and allow diseases to spread stochastically. Our model exhibits some important stylized features of real epidemics, including extreme size variation and temporal heterogeneity, that are difficult to characterize with traditional measures. In particular, our results suggest that when epidemics do occur the basic reproduction number R(0) may bear little relation to their final size. Informed by our model's behavior, we suggest measures for characterizing epidemic thresholds and discuss implications for the control of epidemics.

Communicable Diseases↗

PubMed2005

Human infection patterns and heterogeneous exposure in river blindness.

Here we analyze patterns of human infection with Onchocerca volvulus (the cause of river blindness) in different continents and ecologies. In contrast with some geohelminths and schistosome parasites whose worm burdens typically exhibit a humped pattern with host age, patterns of O. volvulus infection vary markedly with locality. To test the hypothesis that such differences are partly due to heterogeneity in exposure to vector bites, we develop an age- and sex-structured model for intensity of infection, with parasite regulation within humans and vectors. The model is fitted to microfilarial data from savannah villages of northern Cameroon, coffee fincas of central Guatemala, and forest-dwelling communities of southern Venezuela that were recorded before introducing ivermectin treatment. Estimates of transmission and infection loads are compared with entomological and epidemiological field data. Host age- and sex-heterogeneous exposure largely explains locale-specific infection patterns in onchocerciasis (whereas acquired protective immunity has been invoked for other helminth infections). The basic reproductive number, R0, ranges from 5 to 8, which is slightly above estimates for other helminth parasites but well below previously presented values.

Age Factors↗

PubMed2006

Mitigation strategies for pandemic influenza in the United States.

Recent human deaths due to infection by highly pathogenic (H5N1) avian influenza A virus have raised the specter of a devastating pandemic like that of 1917-1918, should this avian virus evolve to become readily transmissible among humans. We introduce and use a large-scale stochastic simulation model to investigate the spread of a pandemic strain of influenza virus through the U.S. population of 281 million individuals for R(0) (the basic reproductive number) from 1.6 to 2.4. We model the impact that a variety of levels and combinations of influenza antiviral agents, vaccines, and modified social mobility (including school closure and travel restrictions) have on the timing and magnitude of this spread. Our simulations demonstrate that, in a highly mobile population, restricting travel after an outbreak is detected is likely to delay slightly the time course of the outbreak without impacting the eventual number ill. For R(0) < 1.9, our model suggests that the rapid production and distribution of vaccines, even if poorly matched to circulating strains, could significantly slow disease spread and limit the number ill to <10% of the population, particularly if children are preferentially vaccinated. Alternatively, the aggressive deployment of several million courses of influenza antiviral agents in a targeted prophylaxis strategy may contain a nascent outbreak with low R(0), provided adequate contact tracing and distribution capacities exist. For higher R(0), we predict that multiple strategies in combination (involving both social and medical interventions) will be required to achieve similar limits on illness rates.

Computer Simulation↗