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Results for “Basic Reproduction Number”

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PubMed1997

Heterogeneities in the transmission of infectious agents: implications for the design of control programs.

From an analysis of the distributions of measures of transmission rates among hosts, we identify an empirical relationship suggesting that, typically, 20% of the host population contributes at least 80% of the net transmission potential, as measured by the basic reproduction number, R0. This is an example of a statistical pattern known as the 20/80 rule. The rule applies to a variety of disease systems, including vector-borne parasites and sexually transmitted pathogens. The rule implies that control programs targeted at the "core" 20% group are potentially highly effective and, conversely, that programs that fail to reach all of this group will be much less effective than expected in reducing levels of infection in the population as a whole.

Animals↗

PubMed2006

Climate disruption and parasite-host dynamics: patterns and processes associated with warming and the frequency of extreme climatic events.

Levels of parasitism and the dynamics of helminth systems is subject to the impact of environmental conditions such that we may expect long term increases in temperature will increase the force of infection and the parasite's basic reproduction number, R0. We postulate that an increase in the force of infection will only lead to an increase in mean intensity of adults when adult parasite mortality is not determined by acquired immunity. Preliminary examination of long term trends of parasites of rabbits and grouse confirm these predictions. Parasite development rate increases with temperature and while laboratory studies indicate this is linear some recent studies indicate that this may be non-linear and would have an important impact on R0. Warming would also reduce the selective pressure for the development of arrestment and this would increase R0 so that in systems like the grouse and Trichostrongylus tenuis this would increase the instability and lead to larger disease outbreaks. Extreme climatic events that act across populations appear important in synchronizing transmission and disease outbreaks, so it is speculated that climate disruption will lead to increased frequency and intensity of disease outbreaks in parasite populations not regulated by acquired immunity.

Animals↗

PubMed2002

Human cytomegalovirus (HCMV) replication dynamics in HCMV-naive and -experienced immunocompromised hosts.

Human cytomegalovirus (HCMV) can infect both HCMV-naive and -experienced transplant patients. In this study, the growth rate of HCMV in HCMV-naive hosts (1.82 units/day; 95% confidence interval [CI], 1.44-2.56 units/day) was shown to be significantly faster than the growth rate of virus in HCMV-experienced hosts undergoing recurrent infection (0.61 units/day; 95% CI, 0.55-0.7 units/day; P<.0001). The basic reproductive number (R(0)) for HCMV-naive liver transplant patients was 15.1 (95% CI, 8.9-44) but was only 2.4 (95% CI, 2.35-2.8) for HCMV-experienced transplant recipients, corresponding to an anti-HCMV immune efficacy of approximately 84%, despite immunosuppressive therapy. The R(0) values suggest that an anti-HCMV drug or vaccine with an efficacy of >93% (95% CI, 89%-98%) is required to eliminate viral growth during infection of HCMV-naive liver transplant recipients, whereas lower efficacy levels are sufficient to reduce the R(0) value to <1 in hosts with prior HCMV immunity.

AIDS-Related Opportunistic Infections↗

PubMed2005

Dynamic models of meningococcal carriage, disease, and the impact of serogroup C conjugate vaccination.

Much interest has surrounded the use of conjugate vaccines in recent years, with the development of vaccines against disease caused by Haemophilus influenzae type b, Neisseria meningitidis, and Streptococcus pneumoniae. These vaccines offer the potential for safe and effective disease control, but some questions remain, particularly regarding the duration and mechanisms of protection and the longer-term impact of vaccination on carriage. In this paper, the authors use data on immunization with serogroup C meningococcal conjugate vaccines in England and Wales to develop and apply a mathematical model to investigate the direct and indirect (herd immunity) effects of a conjugate vaccine program. A realistic, age-structured, dynamic model was developed and parameterized and was fitted to epidemiologic data from England and Wales. The effects of a range of vaccine strategies, including hypothetical scenarios, were investigated. The basic reproduction number was estimated to be 1.36. Catch-up vaccination targeting teenagers generated substantial herd immunity and was important in controlling disease rapidly. The results were sensitive to changes in the assumptions regarding the method of vaccine action, particularly duration of protection and efficacy of vaccination against carriage acquisition. This model can be used to help predict the potential impact of vaccine strategies both in the United Kingdom and elsewhere.

Adolescent↗

PubMed2000

Estimating the immunity coverage required to prevent epidemics in a community of households.

An estimation of the immunity coverage needed to prevent future outbreaks of an infectious disease is considered for a community of households. Data on outbreak size in a sample of households from one epidemic are used to derive maximum likelihood estimates and confidence bounds for parameters of a stochastic model for disease transmission in a community of households. These parameter estimates induce estimates and confidence bounds for the basic reproduction number and the critical immunity coverage, which are the parameters of main interest when aiming at preventing major outbreaks in the future. The case when individuals are homogeneous, apart from the size of their household, is considered in detail. The generalization to the case with variable infectivity, susceptibility and/or mixing behaviour is discussed more briefly. The methods are illustrated with an application to data on influenza in Tecumseh, Michigan.

Journal Article↗

PubMed1991

A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS.

A central aspect in the study of the dynamics of sexually transmitted diseases is that of mixing. The study of the effects of social structure in disease dynamics has received considerable attention over the last few years as a result of the AIDS epidemic. In this paper, we formulate a generalization of the Blythe and Castillo-Chavez social/sexual framework for human interactions through the incorporation of age structure, and derive an explicit expression in terms of a preference function for the general solution to this formulation. We emphasize the role played by proportionate mixing, the only separable solution to this mixing framework, through the discussion of several specific cases, and we formulate an age-structured epidemic model for a single sexually active homosexual population, stratified by risk and age, with arbitrary risk- and age-dependent mixing as well as variable infectivity. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductive number is computed.

Acquired Immunodeficiency Syndrome↗

PubMed2006

Disease emergence in multi-host epidemic models.

Most pathogens are capable of infecting multiple hosts. These multiple hosts provide many avenues for the disease to emerge. In this investigation, we formulate and analyse multi-host epidemic models and determine conditions under which the disease can emerge. In particular, SIS and SIR epidemic models are formulated for a pathogen that can infect n different hosts. The basic reproduction number is computed and shown to increase with n, the number of hosts that can be infected. Therefore, the possibility of disease emergence increases with the number of hosts infected. The SIS model for two hosts is studied in detail. Necessary and sufficient conditions are derived for the global stability of an endemic equilibrium. Numerical examples illustrate the dynamics of the two- and three-host epidemic models. The models have applications to hantavirus in rodents and other zoonotic diseases with multiple hosts.

Algorithms↗

PubMed1995

General framework for comparative quantitative studies on transmission of tick-borne diseases using Lyme borreliosis in Europe as an example.

Models of tick-borne diseases must take account of the particular biological features of ticks that contrast with those of insect vectors. A general framework is proposed that identifies the parameters of the transmission dynamics of tick-borne diseases to allow a quantitative assessment of the relative contributions of different host species and alternative transmission routes to the basic reproductive number, Ro, of such diseases. Taking the particular case of the transmission of the Lyme borreliosis spirochaete, Borrelia burgdorferi, by Ixodes ticks in Europe, and using the best, albeit still inadequate, estimates of the parameter values and a set of empirical data from Thetford Forest, England, we show that squirrels and the transovarial transmission route make quantitatively very significant contributions to Ro. This approach highlights the urgent need for more robust estimates of certain crucial parameter values, particularly the coefficients of transmission between ticks and vertebrates, before we can progress to full models that incorporate seasonality and heterogeneity among host populations for the natural dynamics of transmission of borreliosis and other tick-borne diseases.

Animals↗

PubMed1999

Transmissibility and persistence of oral polio vaccine viruses: implications for the global poliomyelitis eradication initiative.

The global poliomyelitis eradication initiative has been a tremendous success, with current evidence suggesting that wild poliovirus will cease to circulate anywhere in the world soon after the year 2000. As the goal of wild poliovirus eradication is approached, concern has been raised about the potential for persistent transmission of oral polio vaccine (OPV) viruses, as these viruses are known to revert toward wild-type neurovirulence. This paper has been extracted from a document prepared for the World Health Organization on the implications of OPV transmissibility for the strategy of stopping OPV vaccination after global eradication of wild polioviruses. The authors review the empirical evidence on OPV transmissibility available from household and community transmission studies and from mass-vaccination experiences. They then consider theoretical measures of transmissibility and persistence for wild and OPV viruses (secondary attack rate, basic reproduction number, and critical populations' size), to assess whether transmissibility of OPV viruses is sufficient to allow persistence of these viruses after cessation of vaccination. The findings indicate that OPV viruses could persist under various plausible circumstances, and that this potential should be a major consideration when planning the cessation of OPV vaccination.

Disease Reservoirs↗

PubMed1999

Modeling the impact of subclinical measles transmission in vaccinated populations with waning immunity.

An increasing body of evidence suggests that a substantial proportion of individuals who respond to measles vaccine display an antibody boost accompanied by mild or no symptoms on exposure to wild virus. It is unknown whether this emerging class of individuals can support transmission. The epidemiologic consequences of vaccinated individuals able to transmit virus are investigated using a mathematical model. Parameters for this model are estimated using regression analysis on a Canadian serologic data set. The authors confirm that neutralizing antibodies are decaying significantly in absence of circulating virus. Based on a protective threshold plaque reduction neutralization (PRN) titer of 120, the authors estimate the mean duration of vaccine-induced protection in absence of reexposure to be 25 years (95% confidence interval (CI) 18, 48). After long-term absence of circulating virus, the mathematical model predicts that 80% (95% CI 65, 91) of all seroconverted vaccinees have titers below the protective threshold. In this case, elimination of measles virus cannot be achieved by a single-dose routine vaccination strategy if the basic reproduction number in vaccinated individuals exceeds 1.24 (95% CI 1.10, 1.53). For this reason, there is a need to establish the intensity and duration of infectiousness in vaccinated individuals.

Adolescent↗

PubMed2000

Dynamics of HIV-1 viral load rebound among patients with previous suppression of viral replication.

OBJECTIVE: To model the dynamics of HIV-1 rebound in patients receiving suboptimal therapy after suppression of plasma viremia to < 200 copies/ml by triple combination therapy. DESIGN: Mathematical modeling of data from 23 patients switched to indinavir maintenance therapy after viral replication was suppressed with a combination of indinavir, zidovudine and lamivudine. Modeling of HIV-1 rebound among 24 patients on zidovudine/lamivudine maintenance was also performed for comparison. METHODS: Evaluation of slopes of rebound and of their heterogeneity; calculation of the basic reproductive number (Ro, the number of newly infected cells arising from each productively infected cell); regression analyses for predictors of the slope of rebound. RESULTS: Rebound of plasma HIV RNA followed a sigmoid curve with an initial exponential phase. There was significant heterogeneity in the slopes of rebound for individual patients (P < 0.001). In the indinavir maintenance rebounds, the average initial slope was estimated to be 0.587/day (doubling time 1.2 days). The slopes of rebound in patients on zidovudine/lamivudine maintenance tended to be less steep on average (P = 0.025). Among patients taking indinavir maintenance, the average Ro for the initial rebound of viremia was 4.3; in multivariate regressions, the slope of rebound was steeper during early rebound and in patients with higher viral load at the start of triple therapy or a higher CD4 cell count when indinavir monotherapy was initiated. The slope was less steep in patients with a greater increase in the number of CD4 cells during triple therapy. CONCLUSIONS: The rates of viral load increase among patients with viral rebound while receiving less than triple therapy are similar to those reported in patients interrupting therapy. Variability among patients may depend on viral fitness, target cell availability and extent of immune reconstitution.

Adult↗

PubMed2005

Dynamically modeling SARS and other newly emerging respiratory illnesses: past, present, and future.

The emergence and rapid global spread of the severe acute respiratory syndrome (SARS) coronavirus in 2002-2003 prompted efforts by modelers to characterize SARS epidemiology and inform control policies. We overview and discuss models for emerging infectious diseases (EIDs), provide a critical survey of SARS modeling literature, and discuss promising future directions for research. We reconcile discrepancies between published estimates of the basic reproductive number R0 for SARS (a crucial epidemiologic parameter), discuss insights regarding SARS control measures that have emerged uniquely from a modeling approach, and argue that high priorities for future modeling of SARS and similar respiratory EIDs should include informing quarantine policy and better understanding the impact of population heterogeneity on transmission patterns.

Communicable Diseases, Emerging↗

PubMed2003

Curtailing transmission of severe acute respiratory syndrome within a community and its hospital.

Severe acute respiratory syndrome (SARS) has been transmitted extensively within hospitals, and healthcare workers (HCWs) have comprised a large proportion of SARS cases worldwide. We present a stochastic model of a SARS outbreak in a community and its hospital. For a range of basic reproductive numbers (R(0)) corresponding to conditions in different cities (but with emphasis on R(0) approximately 3 as reported for Hong Kong and Singapore), we evaluate contact precautions and case management (quarantine and isolation) as containment measures. Hospital-based contact precautions emerge as the most potent measures, with hospital-wide measures being particularly important if screening of HCWs is inadequate. For R(0) = 3, case isolation alone can control a SARS outbreak only if isolation reduces transmission by at least a factor of four and the mean symptom-onset-to-isolation time is less than 3 days. Delays of a few days in contact tracing and case identification severely degrade the utility of quarantine and isolation, particularly in high-transmission settings. Still more detrimental are delays between the onset of an outbreak and the implementation of control measures; for given control scenarios, our model identifies windows of opportunity beyond which the efficacy of containment efforts is reduced greatly. By considering pathways of transmission in our system, we show that if hospital-based transmission is not halted, measures that reduce community-HCW contact are vital to preventing a widespread epidemic. The implications of our results for future emerging pathogens are discussed.

Community-Acquired Infections↗

PubMed2004

Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour.

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0) and steady-state prevalence (i infinity) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.

Animals↗

PubMed2005

The effect of disease life history on the evolutionary emergence of novel pathogens.

We present a general analytical result for the probability that a newly introduced pathogen will evolve adaptations that allow it to maintain itself within any novel host population, as a function of disease life-history parameters. We demonstrate that this probability of "evolutionary emergence" depends on two key properties of the disease life history: (i) the basic reproduction number and (ii) the expected duration of an infection. These parameters encapsulate all of the relevant information and can be combined in a very simple expression, with estimates for the rates of adaptive mutation, to predict the probability of emergence for any novel pathogen. In general, diseases that initially have a large reproductive number and/or that cause relatively long infections are the most prone to evolutionary adaptation.

Adaptation, Physiological↗

PubMed2006

Seasonal infectious disease epidemiology.

Seasonal change in the incidence of infectious diseases is a common phenomenon in both temperate and tropical climates. However, the mechanisms responsible for seasonal disease incidence, and the epidemiological consequences of seasonality, are poorly understood with rare exception. Standard epidemiological theory and concepts such as the basic reproductive number R0 no longer apply, and the implications for interventions that themselves may be periodic, such as pulse vaccination, have not been formally examined. This paper examines the causes and consequences of seasonality, and in so doing derives several new results concerning vaccination strategy and the interpretation of disease outbreak data. It begins with a brief review of published scientific studies in support of different causes of seasonality in infectious diseases of humans, identifying four principal mechanisms and their association with different routes of transmission. It then describes the consequences of seasonality for R0, disease outbreaks, endemic dynamics and persistence. Finally, a mathematical analysis of routine and pulse vaccination programmes for seasonal infections is presented. The synthesis of seasonal infectious disease epidemiology attempted by this paper highlights the need for further empirical and theoretical work.

Animals↗

PubMed2001

Emerging infectious pathogens of wildlife.

The first part of this paper surveys emerging pathogens of wildlife recorded on the ProMED Web site for a 2-year period between 1998 and 2000. The majority of pathogens recorded as causing disease outbreaks in wildlife were viral in origin. Anthropogenic activities caused the outbreaks in a significant majority of cases. The second part of the paper develops some matrix models for quantifying the basic reproductive number, R(0), for a variety of potential types of emergent pathogen that cause outbreaks in wildlife. These analyses emphasize the sensitivity of R(0) to heterogeneities created by either the spatial structure of the host population, or the ability of the pathogens to utilize multiple host species. At each stage we illustrate how the approach provides insight into the initial dynamics of emergent pathogens such as canine parvovirus, Lyme disease, and West Nile virus in the United States.

Animal Diseases↗

PubMed2004

Infections with varying contact rates: application to varicella.

We develop methods for the analysis of infectious disease data when age-specific contact rates vary over time. Our methods are valid when contact rates vary slowly on the time scale of the infection process, and are applicable to a variety of data types including serial seroprevalence surveys and case reports. The methods exploit approximate endemic equilibria, and require numerical solution of an associated integral equation in age and time. We also estimate summary statistics such as time-dependent analogs of the basic reproduction number and critical immunization threshold. We illustrate the methods with data on varicella (chickenpox) in the United Kingdom.

Adolescent↗