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Results for “Basic Reproduction Number”

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PubMed2006

Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus.

This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host-vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the host-vector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, R(0). We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters R(0) and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, R(0) estimates for six common North American bird species indicate that all would be effective outbreak hosts.

Animals↗

PubMed1996

Field epidemiology of an outbreak of dengue fever in Charters Towers, Queensland: are insect screens protective?

Between March and July 1993 a dengue virus epidemic swept through Charters Towers, a rural North Queensland mining community of 10,000. This clearly delineated outbreak provided an ideal opportunity to carry out one of the few field epidemiological studies of dengue in Australia. The epicurve was consistent with that of a point source outbreak, 18 weeks in duration and peaking at four weeks. A basic reproduction number for the dengue epidemic of 1.99 indicates a similar rate of spread to that found in dengue epidemics overseas. A female-to-male sex ratio of 1.7:1 was obtained for the 238 cases identified. An age- and sex-matched retrospective case-control study showed that cases were significantly more likely to live in unscreened houses than were controls (McNemar chi 2 = 56.1 df, P < 0.0001). Despite being generally accepted, an association between insect screens and a reduced incidence of mosquito-borne diseases has not previously been demonstrated in Australia. We speculate that unscreened housing facilitates the initial spread of a dengue epidemic.

Adolescent↗

PubMed2006

Predictive models of control strategies involved in containing indoor airborne infections.

Recently developed control measure modeling approaches for containing airborne infections, including engineering controls with respiratory protection and public health interventions, are readily amenable to an integrated-scale analysis. Here we show that such models can be derived from an integrated-scale analysis generated from three different types of functional relationship: Wells-Riley mathematical model, competing-risks model, and Von Foerster equation, both of the key epidemiological determinants involved and of the functional connections between them. We examine mathematically the impact of engineering control measures such as enhanced air exchange and air filtration rates with personal masking combined with public health interventions such as vaccination, isolation, and contact tracing in containing the spread of indoor airborne infections including influenza, chickenpox, measles, and severe acute respiratory syndrome (SARS). If enhanced engineering controls could reduce the basic reproductive number (R0) below 1.60 for chickenpox and 3 for measles, our simulations show that in such a prepared response with public health interventions would have a high probability of containing the indoor airborne infections. Combinations of engineering control measures and public health interventions could moderately contain influenza strains with an R0 as high as 4. Our analysis indicates that effective isolation of symptomatic patients with low-efficacy contact tracing is sufficient to control a SARS outbreak. We suggest that a valuable added dimension to public health inventions could be provided by systematically quantifying transmissibility and proportion of asymptomatic infection of indoor airborne infection. Practical Implications We have developed a flexible mathematical model that can help determine the best intervention strategies for containing indoor airborne infections. The approach presented here is scalable and can be extended to include additional control efficacies. If a newly emergent airborne infection should appear, the model could be quickly calibrated to data and intervention options at the early stage of the outbreak. Data could be provided from the field to estimate value of R0, the serial interval between cases, the distributions of the latent, incubation, and infectious periods, case fatality rates, and secondary spread within important mixing groups. The combination of enhanced engineering control measures and assigned effective public health interventions would have a high probability for containing airborne infection.

Air Pollution, Indoor↗

PubMed2001

The epidemic behavior of the hepatitis C virus.

Hepatitis C virus (HCV) is a leading worldwide cause of liver disease. Here, we use a new model of HCV spread to investigate the epidemic behavior of the virus and to estimate its basic reproductive number from gene sequence data. We find significant differences in epidemic behavior among HCV subtypes and suggest that these differences are largely the result of subtype-specific transmission patterns. Our model builds a bridge between the disciplines of population genetics and mathematical epidemiology by using pathogen gene sequences to infer the population dynamic history of an infectious disease.

Endemic Diseases↗

PubMed2005

Containing pandemic influenza at the source.

Highly pathogenic avian influenza A (subtype H5N1) is threatening to cause a human pandemic of potentially devastating proportions. We used a stochastic influenza simulation model for rural Southeast Asia to investigate the effectiveness of targeted antiviral prophylaxis, quarantine, and pre-vaccination in containing an emerging influenza strain at the source. If the basic reproductive number (R0) was below 1.60, our simulations showed that a prepared response with targeted antivirals would have a high probability of containing the disease. In that case, an antiviral agent stockpile on the order of 100,000 to 1 million courses for treatment and prophylaxis would be sufficient. If pre-vaccination occurred, then targeted antiviral prophylaxis could be effective for containing strains with an R0 as high as 2.1. Combinations of targeted antiviral prophylaxis, pre-vaccination, and quarantine could contain strains with an R(0) as high as 2.4.

Adolescent↗

PubMed2006

Kinetics of influenza A virus infection in humans.

Currently, little is known about the viral kinetics of influenza A during infection within an individual. We utilize a series of mathematical models of increasing complexity, which incorporate target cell limitation and the innate interferon response, to examine influenza A virus kinetics in the upper respiratory tracts of experimentally infected adults. The models were fit to data from an experimental H1N1 influenza A/Hong Kong/123/77 infection and suggest that it is important to include the eclipse phase of the viral life cycle in viral dynamic models. Doing so, we estimate that after a delay of approximately 6 h, infected cells begin producing influenza virus and continue to do so for approximately 5 h. The average lifetime of infected cells is approximately 11 h, and the half-life of free infectious virus is approximately 3 h. We calculated the basic reproductive number, R(0), which indicated that a single infected cell could produce approximately 22 new productive infections. This suggests that antiviral treatments have a large hurdle to overcome in moderating symptoms and limiting infectiousness and that treatment has to be initiated as early as possible. For about 50% of patients, the curve of viral titer versus time has two peaks. This bimodal behavior can be explained by incorporating the antiviral effects of interferon into the model. Our model also compared well to an additional data set on viral titer after experimental infection and treatment with the neuraminidase inhibitor zanamivir, which suggests that such models may prove useful in estimating the efficacies of different antiviral therapies for influenza A infection.

Administration, Intranasal↗

PubMed2002

The geographical and temporal evolution of sexually transmitted disease epidemics.

In developing appropriate interventions to control sexually transmitted infections (STIs) it is important to understand the distribution of infections, and how this distribution is influenced by the dynamic nature of epidemics. The epidemiology of STIs has been described as a series of phases, which loosely positions a population within the history of an epidemic. The relation between a mathematical theory describing STI epidemiology and the taxonomy of "phases" is explored in this review of the transmission dynamics of STIs. The likelihood of spread and persistence of infection depends upon the basic reproductive number, whereas the endemic prevalence of infection depends upon the way in which heterogeneity in risk focuses the density dependent constraints limiting the spread of infection. All interventions aimed at reducing the prevalence and incidence of infection must act through the reproductive number. The key parameters determining the reproductive number and the relevance of risk behaviours depend upon the biology of the particular infection. The division between high transmission probability, short duration infections and low transmission probability, long duration infections is explored.

Disease Outbreaks↗

PubMed2004

Statics and dynamics of malaria infection in Anopheles mosquitoes.

The classic formulae in malaria epidemiology are reviewed that relate entomological parameters to malaria transmission, including mosquito survivorship and age-at-infection, the stability index (S), the human blood index (HBI), proportion of infected mosquitoes, the sporozoite rate, the entomological inoculation rate (EIR), vectorial capacity (C) and the basic reproductive number (R0). The synthesis emphasizes the relationships among classic formulae and reformulates a simple dynamic model for the proportion of infected humans. The classic formulae are related to formulae from cyclical feeding models, and some inconsistencies are noted. The classic formulae are used to to illustrate how malaria control reduces malaria transmission and show that increased mosquito mortality has an effect even larger than was proposed by Macdonald in the 1950's.

Animals↗

PubMed2006

Key transmission parameters of an institutional outbreak during the 1918 influenza pandemic estimated by mathematical modelling.

AIM: To estimate the key transmission parameters associated with an outbreak of pandemic influenza in an institutional setting (New Zealand 1918). METHODS: Historical morbidity and mortality data were obtained from the report of the medical officer for a large military camp. A susceptible-exposed-infectious-recovered epidemiological model was solved numerically to find a range of best-fit estimates for key epidemic parameters and an incidence curve. Mortality data were subsequently modelled by performing a convolution of incidence distribution with a best-fit incidence-mortality lag distribution. RESULTS: Basic reproduction number (R0) values for three possible scenarios ranged between 1.3, and 3.1, and corresponding average latent period and infectious period estimates ranged between 0.7 and 1.3 days, and 0.2 and 0.3 days respectively. The mean and median best-estimate incidence-mortality lag periods were 6.9 and 6.6 days respectively. This delay is consistent with secondary bacterial pneumonia being a relatively important cause of death in this predominantly young male population. CONCLUSION: These R0 estimates are broadly consistent with others made for the 1918 influenza pandemic and are not particularly large relative to some other infectious diseases. This finding suggests that if a novel influenza strain of similar virulence emerged then it could potentially be controlled through the prompt use of major public health measures.

Adult↗

PubMed2006

Reducing the impact of the next influenza pandemic using household-based public health interventions.

BACKGROUND: The outbreak of highly pathogenic H5N1 influenza in domestic poultry and wild birds has caused global concern over the possible evolution of a novel human strain [1]. If such a strain emerges, and is not controlled at source [2,3], a pandemic is likely to result. Health policy in most countries will then be focused on reducing morbidity and mortality. METHODS AND FINDINGS: We estimate the expected reduction in primary attack rates for different household-based interventions using a mathematical model of influenza transmission within and between households. We show that, for lower transmissibility strains [2,4], the combination of household-based quarantine, isolation of cases outside the household, and targeted prophylactic use of anti-virals will be highly effective and likely feasible across a range of plausible transmission scenarios. For example, for a basic reproductive number (the average number of people infected by a typically infectious individual in an otherwise susceptible population) of 1.8, assuming only 50% compliance, this combination could reduce the infection (symptomatic) attack rate from 74% (49%) to 40% (27%), requiring peak quarantine and isolation levels of 6.2% and 0.8% of the population, respectively, and an overall anti-viral stockpile of 3.9 doses per member of the population. Although contact tracing may be additionally effective, the resources required make it impractical in most scenarios. CONCLUSIONS: National influenza pandemic preparedness plans currently focus on reducing the impact associated with a constant attack rate, rather than on reducing transmission. Our findings suggest that the additional benefits and resource requirements of household-based interventions in reducing average levels of transmission should also be considered, even when expected levels of compliance are only moderate.

Antiviral Agents↗

PubMed2003

Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil.

OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengue-infested area. METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in S o Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS: Currently there is a great number of non-vaccinated people living in Aedes aegypti infested area in the state of São Paulo.

Aedes↗

PubMed2002

Influence of nonsystemic transmission on the epidemiology of insect borne arboviruses: a case study of vesicular stomatitis epidemiology in the western United States.

Nonsystemic transmission, where a pathogen is transmitted between infected and uninfected vectors without the vertebrate host becoming viremic, may provide an explanation for transmission in systems where the vertebrate hosts have been difficult to identify. This transmission pathway had been previously demonstrated for tick-borne viruses and bacteria, but the recent demonstration for Simulium and vesicular stomatitis virus is the first for a blood-feeding insect. The epidemiology of vesicular stomatitis viruses has been difficult to understand, and nonsystemic transmission may be important. We use mathematical formulations of the basic reproduction number, R(0), to compare systemic and nonsystemic transmission. The absence of a latent period before host infectiousness in nonsystemic transmission may allow a more rapid increase in prevalence in the biting flies early in the development of a new outbreak. Aggregation of flies between hosts and at favored feeding sites on hosts will be important, but further data on nonsystemic transmission as a function of space and time are required to fully assess this pathway. The data needed to compare the two pathways and their relative roles in virus epidemiology are discussed.

Animals↗

PubMed2006

Dynamics of prion disease transmission in mule deer.

Chronic wasting disease (CWD), a contagious prion disease of the deer family, has the potential to severely harm deer populations and disrupt ecosystems where deer occur in abundance. Consequently, understanding the dynamics of this emerging infectious disease, and particularly the dynamics of its transmission, has emerged as an important challenge for contemporary ecologists and wildlife managers. Although CWD is contagious among deer, the relative importance of pathways for its transmission remains unclear. We developed seven competing models, and then used data from two CWD outbreaks in captive mule deer and model selection to compare them. We found that models portraying indirect transmission through the environment had 3.8 times more support in the data than models representing transmission by direct contact between infected and susceptible deer. Model-averaged estimates of the basic reproductive number (R0) were 1.3 or greater, indicating likely local persistence of CWD in natural populations under conditions resembling those we studied. Our findings demonstrate the apparent importance of indirect, environmental transmission in CWD and the challenges this presents for controlling the disease.

Animals↗

PubMed2026

The Re-Emergence of Bundibugyo Ebolavirus in Uganda and the Democratic Republic of Congo: Epidemiological Drivers, Response Strategies, and Implications for Global Health Security.

Bundibugyo ebolavirus (BDBV) is one of the least studied species within the genus Orthoebolavirus (family Filoviridae), despite its capacity to cause severe Ebola virus disease (EVD) with substantial mortality. First identified during a 2007-2008 outbreak in Bundibugyo District, western Uganda (149 reported cases, 37 deaths; case-fatality rate [CFR] approximately 25-36%), BDBV re-emerged in 2012 in Orientale Province, Democratic Republic of the Congo (DRC) (57-59 cases, 29-34 deaths; CFR 34-58%), before resurfacing in Ituri Province, DRC, in April-May 2026. By 11 August 2026, this third outbreak had grown to 4566 laboratory-confirmed cases and 2128 deaths (CFR ≈ 47%) across five DRC provinces and Uganda, becoming the largest, fastest-growing BDBV epidemic on record and the second-largest Ebola-family outbreak overall. This narrative review, not a systematic review or meta-analysis, summarizes peer-reviewed literature, preprints, and official situation reports from WHO, Africa CDC, US CDC, ECDC, and national health ministries, identified through PubMed, Scopus, Web of Science, Google Scholar, and Embase from inception to 12 August 2026, to examine BDBV historical evolution, virology and pathogenesis, drivers of re-emergence, surveillance and response, therapeutic and vaccine gaps, and global health security implications. The 2026 outbreak, unfolding amid conflict and mass displacement in eastern DRC, has been marked by an estimated basic reproduction number of 1.4-2.1 (central estimate 1.71), disproportionate infection among healthcare workers (7.2% of confirmed cases in DRC, 20% in Uganda), and the continued absence of licensed BDBV-specific vaccines or therapeutics. Findings underscore the need for sustained genomic and ecological surveillance, decentralized rapid diagnostics, broadly protective pan-filovirus vaccines, conflict-sensitive response strategies, and strengthened Uganda-DRC collaboration. Because the evidence base for the ongoing outbreak remains preliminary, findings should be interpreted cautiously and revisited as further peer-reviewed data emerge.

Bundibugyo ebolavirus↗

PubMed2004

Model parameters and outbreak control for SARS.

Control of the 2002-2003 severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R0. We estimated the distribution of the reproductive number R0 under perfect isolation conditions. The distribution lies in the interquartile range 0.19-1.08, with a median of 0.49. Even though the median of R0 is <1, we found that 25% of our R0 distribution lies at R0 > 1, even with perfect isolation. This implies the need to simultaneously apply more than one method of control.

Communicable Disease Control↗

PubMed1999

Effect of chemotherapy on malaria transmission among Yanomami Amerindians: simulated consequences of placebo treatment.

To determine whether chemotherapy effectively reduces Plasmodium falciparum malaria transmission in isolated human populations, we followed two abrupt sequential outbreaks of malaria infection among Yanomami Amerindians and modeled the effect of chemotherapy and the consequences if no drug was available. A Macdonald-type mathematical model demonstrated that both outbreaks comprised a single epidemic event linked by an invisible outbreak in vector mosquitoes. The basic reproductive number, R0, from fitted values based on the treated epidemic was 2 during the initial phase of the epidemic, and waned as vector density decreased with the onset of the dry season. In the observed epidemic, 60 (45%) of 132 village residents were affected, and the treated outbreak ended after two months. Although the initial chemotherapy regimen was only marginally effective, the duration of human infectivity was reduced from an expected nine months to two weeks. In the absence of this intervention, the initial R0 value would have been 40, more than 60% of the population would have been infected, and more than 30% would have remained parasitemic until the next rainy season (about six months later). Another outbreak would then have ensued, and malaria probably would have remained endemic in this village. Our simulated placebo treatment permits us to conclude that even partially effective chemotherapeutic interventions, such as those in our study, interrupt serial transmission of P. falciparum among isolated human populations that are exposed to infection seasonally.

Animals↗

PubMed1999

Review of intra-host models of malaria.

Intra-host models of malaria (and some related models of trypanosomiasis) are reviewed. A first section gives a short description of the different models, their purposes and the authors' conclusions. A second section discusses some common issues, including intra-host populations, the intra-host basic reproduction number (R0) and growth rates, density regulation mechanisms (including acquired immunity), and the models' behaviour compared to that of Plasmodium falciparum in man.

Animals↗

PubMed2001

A model of Gambian sleeping sickness with open vector populations.

A compartmental model of Gambian sleeping sickness is described that takes into account density-dependent migratory flows of infected flies. Equilibrium and stability theorems are given which show that with a basic reproduction number R0 below unity, then in the absence of reinvasion the disease goes to extinction. However, even a low prevalence rate among reinvading flies can then bring about significant equilibrium prevalence rates among humans. For a set of realistic parameter values we show that even in the case of a virulent parasite that keeps infected individuals in the first stage for as little as 4 or 8 months (durations for which there would be extinction with no infected reinvading flies) there is a prevalence rate in the range 13.0-36.9%, depending on whether 1 or 2% of reinvading flies are infected. A rate of convergence of the population dynamics is introduced and is interpreted in terms of a halving time of the infected population. It is argued that the persistence and/or extension of Gambian sleeping sickness foci could be due either to a continuous reinvasion of infected flies or to slow dynamics.

Animals↗