SEARCH · PubMed Health

Results for “Basic Reproduction Number”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11Linked to original sources

PubMed2001

A mathematical treatment of AIDS and condom use.

In this paper we examine the impact of condom use on the sexual transmission of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) amongst a homogeneously mixing male homosexual population. We first derive a multi-group SIR-type model of HIV/AIDS transmission where the homosexual population is split into subgroups according to frequency of condom use. Both susceptible and infected individuals can transfer between the different groups. We then discuss in detail an important special case of this model which includes two risk groups and perform an equilibrium and stability analysis for this special case. Our analysis shows that this model can exhibit unusual behaviour. As normal, if the basic reproduction number, R0, is greater than unity then there is a unique disease-free equilibrium which is locally unstable and a unique endemic equilibrium. However, when R0 is less than unity two endemic equilibrium solutions can also co-exist simultaneously with the disease-free solution which is locally stable. Numerical simulations using realistic parameter values confirm this and we find that in certain circumstances the disease-free solution and one of the endemic solutions are both locally asymptotically stable, while the other endemic solution is unstable. This unusual behaviour has important implications for control of the disease as reducing R0 to less than unity no longer guarantees eradication of the disease. For a restricted special case of this two-group model we show that there is only the disease-free equilibrium for R0 < or = 1 which is globally stable. For R0 > 1 the disease-free equilibrium is unstable and there is a unique endemic equilibrium which is locally stable. We then attempt to fit the model to HIV and AIDS incidence data from San Francisco, USA. The paper concludes with a brief discussion.

Acquired Immunodeficiency Syndrome↗

PubMed2003

The transmission dynamics of canine American cutaneous leishmaniasis in Huánuco, Peru.

The epidemiology of canine American cutaneous leishmaniasis (ACL) due to Leishmania (Viannia) spp. was investigated in Huánuco, Peru to 1) describe the natural course of canine L. (Viannia) infections and 2) assess the role of domestic dogs as ACL reservoir hosts. Over a three-year period 1,022 dogs were surveyed, with cumulative village L. (Viannia) prevalence being 26% (range = 0-100%). The incidence of L. (Viannia) was estimated to be 0.285 dogs/year (95% confidence interval [CI] = 0.160-0.410) using cross-sectional data and 0.291 dogs/year (95% CI = 0.195-0.387) using data from 108 dogs that were surveyed prospectively. The recovery rate was estimated to be 0.456 dogs/year (95% CI = 0.050-0.862) and 0.520 dogs/year (95% CI = 0.302-0.738), respectively. Using those findings, the basic reproduction number was estimated to be R0 approximately to 1.9; if dogs were the principal ACL reservoirs, the mean yearly effort (i.e., coverage or elimination) of a dog control intervention (e.g., collaring, culling, or vaccination) to ensure the elimination of L. (Viannia) spp. transmission would be as low as 47%.

Animals↗

PubMed2003

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil.

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Aedes↗

PubMed2005

Outbreaks caused by parvovirus B19 in three Portuguese schools.

This paper reports the study of outbreaks of an acute exanthematous disease among children of three schools in the municipality of Braga (Portugal). Laboratory tests were performed for five cases, showing that the disease was not due to infection by measles or rubella virus, and infection with parvovirus B19 was confirmed. There were 41 cases in children: 12 in the kindergarten, 17 in the secondary school and 12 in the primary school. There was only one case in a staff member, who worked in the kindergarten. Eight cases were identified among household contacts; two of them were brothers, one from the kindergarten and another from the secondary school, where the outbreak occurred after the kindergarten outbreak. The estimated values of the basic reproduction number R0 were very low and it is very likely that asymptomatic infectious cases have occurred. The local health authority produced written documents and met with staff members and parents. Primary healthcare facilities and the obstetric department of the local hospital were also informed. As we are approaching the elimination of measles in Portugal and the rest of Europe, with very high vaccine coverage, it is very likely that a high proportion of infectious non-vesicular exanthemas will be due to B19 infections. This is to be taken into account in the design and conduct of surveillance activities, in the context of measles and rubella elimination programmes.

Child↗

PubMed2005

Towards a simulation environment for modeling of local influenza outbreaks.

OBJECTIVE: To analyze the design of a simulation environment for dynamic prediction of influenza transmission in local communities. METHODS: The technique trade-off method was used to identify and analyze basic design requirements on a simulation environment for modeling of influenza transmission. Data were collected through literature review and interviews with infectious disease experts. The identified requirements were matched to a set of design issues for the simulation environment,and a high-resolution prototype was implemented. RESULTS: Basic reproductive numbers for influenza transmission in a set of Swedish municipalities were calculated. Tradeoffs were necessary in the design between a focus on reproductive numbers vs. case fatality proportions, algorithm validity vs. model adaptability, and specificity in population description vs. generalizability. CONCLUSION: Computer-based simulations can become important tools for local authorities preparing for influenza outbreaks. Balanced tradeoffs between model detail and public health effectiveness are important in simulation environment design.

Adolescent↗

PubMed1994

Role of the primary infection in epidemics of HIV infection in gay cohorts.

A review of the data on infectivity per contact for transmission of the HIV suggests that the infectivity may be on the order of 0.1-0.3 per anal intercourse in the period of the initial infection, 10(-4) to 10(-3) in the long asymptomatic period, and 10(-3) to 10(-2) in the period leading into AIDS. The pattern of high contagiousness during the primary infection followed by a large drop in infectiousness may explain the pattern of epidemic spread seen in male homosexual cohorts in the early years of the epidemic. Simulations of cohorts of homosexual males, using that range of parameter values, indicate the following: (a) The initial fast rise and then more or less rapid flattening of the incidence curve of seropositives is primarily due to rapid initial spread, yielding a group of infecteds all of whom pass into the low infectivity asymptomatic period at close to the same time. All this occurs only if the basic reproduction number for the primary infection is > 1. (b) The behavioral changes that have been reported all started after the incidence of new infections began to fall, too late to have a major effect on the initial rise. The behavioral changes had a major effect in slowing down the subsequent rise in the number of seropositives. (c) High activity groups play an important role in the early rapid rise of the epidemic. However, it is not likely that the rapid decrease in rate of growth of seropositives is solely due to saturation of these very high activity groups. Although the evidence for this interpretation of the role of the primary infection is not conclusive, its implications for prevention and for vaccine trials are so markedly different from those of other interpretations that we consider it to be an important hypothesis for further testing.

Cohort Studies↗

PubMed1997

An analysis of foot-and-mouth-disease epidemics in the UK.

There was a major epidemic of the foot-and-mouth-disease virus among cattle herds in the UK in 1967-68 which showed a very rapid early spread, a much slower later spread, and eventually infected 12% of herds in the core epidemic area. A simple discrete-time version of a susceptible-latent-infectious-removed epidemiological model is used to generate a set of estimates of the transmission rate. This parameter has high values over the first few days, then the values are lower and they subsequently decline. The early high values are consistent with the view that unusual meteorological conditions produced exceptionally good conditions for wind-borne spread of the virus over the first few days. The corresponding basic reproduction number, Rzero, is estimated as 38.4. Subsequent low values of the transmission rate correspond to a value of Rzero of 2.0; this is within the range of estimates made from the observed ratio of secondary to primary outbreaks for 25 other epidemics. Prophylactic control measures, such as vaccination, would have to be extremely effective to prevent epidemics with the higher Rzero value.

Animals↗

PubMed1997

The epidemiology of canine leishmaniasis: transmission rates estimated from a cohort study in Amazonian Brazil.

We estimate the incidence rate, serological conversion rate and basic case reproduction number (R0) of Leishmania infantum from a cohort study of 126 domestic dogs exposed to natural infection rates over 2 years on Marajó Island, Pará State, Brazil. The analysis includes new methods for (1) determining the number of seropositives in cross-sectional serological data, (2) identifying seroconversions in longitudinal studies, based on both the number of antibody units and their rate of change through time, (3) estimating incidence and serological pre-patent periods and (4) calculating R0 for a potentially fatal, vector-borne disease under seasonal transmission. Longitudinal and cross-sectional serological (ELISA) analyses gave similar estimates of the proportion of dogs positive. However, longitudinal analysis allowed the calculation of pre-patent periods, and hence the more accurate estimation of incidence: an infection-conversion model fitted by maximum likelihood to serological data yielded seasonally varying per capita incidence rates with a mean of 8.66 x 10(-3)/day (mean time to infection 115 days, 95% C.L. 107-126 days), and a median pre-patent period of 94 (95% C.L. 82-111) days. These results were used in conjunction with theory and dog demographic data to estimate the basic reproduction number, R0, as 5.9 (95% C.L. 4.4-7.4). R0 is a determinant of the scale of the leishmaniasis control problem, and we comment on the options for control.

Animals↗

PubMed1997

Infectious disease persistence when transmission varies seasonally.

The generation reproduction number, R0, is the fundamental parameter of population biology. Communicable disease epidemiology has adopted R0 as the threshold parameter, called the basic case reproduction number (or ratio). In deterministic models, R0 must be greater than 1 for a pathogen to persist in its host population. Some standard methods of estimating R0 for an endemic disease require measures of incidence, and the theory underpinning these estimators assumes that incidence is constant through time. When transmission varies periodically (e.g., seasonally), as it does for most pathogens, it should be possible to express the criterion for long-term persistence in terms of some average transmission (and hence incidence) rate. A priori, there are reasons to believe that either the arithmetic mean or the geometric mean transmission rate may be correct. By considering the problem in terms of the real-time growth rate of the population, we are able to demonstrate formally that, to a very good approximation, the arithmetic mean transmission rate gives the correct answer for a general class of infection functions. The geometric mean applies only to a highly restricted set of cases. The appropriate threshold parameter can be calculated from the average transmission rate, and we discuss ways of doing so in the context of an endemic vector-borne disease, canine leishmaniasis.

Animals↗

PubMed2025

Estimating Re and overdispersion in secondary cases from the size of identical sequence clusters of SARS-CoV-2.

The wealth of genomic data that was generated during the COVID-19 pandemic provides an exceptional opportunity to obtain information on the transmission of SARS-CoV-2. Specifically, there is great interest to better understand how the effective reproduction number [Formula: see text] and the overdispersion of secondary cases, which can be quantified by the negative binomial dispersion parameter k, changed over time and across regions and viral variants. The aim of our study was to develop a Bayesian framework to infer [Formula: see text] and k from viral sequence data. First, we developed a mathematical model for the distribution of the size of identical sequence clusters, in which we integrated viral transmission, the mutation rate of the virus, and incomplete case-detection. Second, we implemented this model within a Bayesian inference framework, allowing the estimation of [Formula: see text] and k from genomic data only. We validated this model in a simulation study. Third, we identified clusters of identical sequences in all SARS-CoV-2 sequences in 2021 from Switzerland, Denmark, and Germany that were available on GISAID. We obtained monthly estimates of the posterior distribution of [Formula: see text] and k, with the resulting [Formula: see text] estimates slightly lower than estimates obtained by other methods, and k comparable with previous results. We found comparatively higher estimates of k in Denmark which suggests less opportunities for superspreading and more controlled transmission compared to the other countries in 2021. Our model included an estimation of the case detection and sampling probability, but the estimates obtained had large uncertainty, reflecting the difficulty of estimating these parameters simultaneously. Our study presents a novel method to infer information on the transmission of infectious diseases and its heterogeneity using genomic data. With increasing availability of sequences of pathogens in the future, we expect that our method has the potential to provide new insights into the transmission and the overdispersion in secondary cases of other pathogens.

COVID-19↗

PubMed1995

Epidemiology of canine leishmaniasis in the Madrid region, Spain.

A cross-sectional serological survey was carried out in the Madrid Autonomous Region (Comunidad de Madrid) in order to study and describe canine leishmaniasis epidemiology. The presence of leishmaniasis-specific antibodies was ascertained by immunofluorescence testing, 591 dogs were screened, revealing a prevalence of 5.25% (95% confidence interval 7.4-3.6), with no difference being encountered between rural and periurban areas. Age-specific prevalence exhibits a peak at 2-3 years and another at 7-8 years. Incidence or force of infection by occupation is as follows: pet dogs 0.059 (95% confidence interval 0.009-0.108) and working dogs 0.035 (95% confidence interval 0.012-0.057), there being a ratio between infection rates of 1.7, viz., indicating a 70% greater risk of infection among pet than among working dogs. The basic case reproduction number R0 is 1.06, suggesting that very intense control measures would not be needed for a drop in prevalence and incidence of infection to be achieved.

Age Factors↗

PubMed1996

Immunization coverage required to prevent outbreaks of dog rabies.

WHO recommends that 70% of dogs in a population should be immunized to eliminate or prevent outbreaks of rabies. This critical percentage (pc) has been established empirically from observations on the relationship between vaccination coverage and rabies incidence in dog populations around the world. Here, by contrast, we estimate pc by using epidemic theory, together with data available from four outbreaks in urban and rural areas of the USA, Mexico, Malaysia and Indonesia. From the rate of increase of cases at the beginning of these epidemics, we obtain estimates of the basic case reproduction number of infection, R0, in the range 1.62-2.33, implying that pc lies between 39% and 57%. The errors attached to these estimates of pc suggest that the recommended coverage of 70% would prevent a major outbreak of rabies on no fewer than 96.5% of occasions.

Animals↗

PubMed2006

The influence of nurse cohorting on hand hygiene effectiveness.

BACKGROUND: Direct contact between health care staff and patients is generally considered to be the primary route by which most exogenously-acquired infections spread within and between wards. Handwashing is therefore perceived to be the single most important infection control measure that can be adopted, with the continuing high infection rates generally attributed to poor hand hygiene compliance. METHODS: Through the use of simple mathematical models, this paper demonstrates that under conditions of high patient occupancy or understaffing, handwashing alone is unlikely to prevent the transmission of infection. CONCLUSIONS: The study demonstrates that applying strict nurse cohorting in combination with good hygiene practice is likely to be a more effective method of reducing transmission of infection in hospitals.

Attitude of Health Personnel↗

PubMed2006

Endemic threshold results in an age-duration-structured population model for HIV infection.

In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R(0) is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.

Age Factors↗

PubMed2000

Epidemiology and optimal foraging: modelling the ideal free distribution of insect vectors.

Existing models of the basic case reproduction number (R0) for vector-borne diseases assume (i) that the distribution of vectors over the susceptible host species is homogeneous and (ii) that the biting preference for the susceptible host species rather than other potential hosts is a constant. Empirical evidence contradicts both assumptions, with important consequences for disease transmission. In this paper we develop an Ideal Free Distribution (IFD) model of host choice by blood-sucking insects, predicated on the argument that vectors must have evolved to choose the least defensive hosts in order to maximize their feeding success. From a re-analysis of existing data, we demonstrate that the interference constant, m, of the IFD can vary between host species. As a result, the predicted distribution of insects over hosts has 2 desirable and intuitively plausible behaviours: that it is heterogeneous both within and between host species; and that the intensity of heterogeneity varies with host and vector density. When the IFD model is incorporated into R0, the relationship with the vector:host ratio becomes non-linear. If correct, the IFD could add considerable realism to models which seek to predict the effect of these ecological parameters on disease transmission as they vary naturally (e.g. through seasonality in vector density or host population movement) or as a consequence of artificial manipulation (e.g. zooprophylaxis, vector control). It raises the possibility of targeting transmission hot spots with greater accuracy and concomitant reduction in control effort. The robustness of the model to simplifying assumptions is discussed.

Animals↗

PubMed2002

A continental risk map for malaria mosquito (Diptera: Culicidae) vectors in Europe.

Although malaria was officially declared eradicated from Europe in 1975, its former vectors, mainly members of the Anopheles maculipennis (Meigen) complex, are still distributed throughout the continent. The present situation of Anophelism without malaria indicates that current socio-economic and environmental conditions maintain the basic case reproduction number, Ro, below 1. Recently, it has been speculated that predicted climate changes may increase anopheline abundance and biting rates (as well as reduce the Plasmodium parasite extrinsic incubation period), allowing the reemergence of malaria transmission in Europe. As a preliminary step toward predicting future scenarios, we have constructed models to test whether the current distribution of the five former European malaria vectors [An. atroparvus (Van Thiel),An. labranchiae (Falleroni), An. messeae (Swellengrebel & De Buck), An. sacharovi (Favr) and An. superpictus (Grassi)] can be explained by environmental parameters, including climate. Multivariate logistic regression models using climate surfaces derived from interpolation of meteorological station data (resolution 0.5 x 0.5 degrees) and remotely sensed land cover (resolution 1 x 1 km) were fitted to 1,833 reported observations of the presence and absence of each species across Europe. These relatively crude statistical models predicted presence and absence with a sensitivity of 74-85.7% and specificity of 73.4-98.1% (with climate a significantly better predictor than land cover type). A geographically independent validation of the models gave a sensitivity of 72.9-88.5% and a specificity of 72.7-99.6%. This allowed us to generate risk maps for each species across Europe. Assuming that high risk equates with the potential for high abundance, these models should permit the development of risk maps for European mosquitoes under future climate scenarios. These techniques would be equally useful for estimating the risk of reemergence in other nonendemic areas such as the United States and Australia, as well as changes to risk within endemic areas.

Animals↗

PubMed1996

The emergence of HIV/AIDS in Africa.

The recent spread of HIV/AIDS in Africa must be seen in the broader context of emerging infectious diseases, whose epidemiology results from changes in the equilibrium between the agent, the host, and the environment. For sexually transmitted agents such as HIV, epidemic spread requires a high basic reproductive rate (number of secondary cases generated by one primary case), which is itself dependent on the rate of change of sex partners, the transmissibility of the agent, and the duration of infectiousness. Factors relating to the agent which may have influenced the spread of HIV in Africa are viral types (HIV-1, HIV-2) and subtypes, of which at least 9 exist for the main group of HIV-1. Major host factors include sexual behaviour and sexual networks, commercial sex, sexually transmitted diseases, condom use, and circumcision status in males. Most difficult to study are environmental factors in the broadest sense, such as behavioral norms, poverty, migration, and HIV/AIDS prevention efforts. Any model attempting to explain HIV/AIDS emergence must account for the extreme heterogeneity of the epidemic within the African continent, and must be relevant to the application of more effective interventions. Although descriptive and analytic epidemiology remain necessary, intervention-oriented research on HIV/AIDS is now the priority in Africa.

Acquired Immunodeficiency Syndrome↗

PubMed1993

Monitoring trypanosomiasis in space and time.

The paper examines the possible contributions to be made by Geographic Information Systems (GIS) to studies on human and animal trypanosomiasis in Africa. The epidemiological characteristics of trypanosomiasis are reviewed in the light of the formula for the basic reproductive rate or number of vector-borne diseases. The paper then describes how important biological characteristics of the vectors of trypanosomiasis in West Africa may be monitored using data from the NOAA series of meteorological satellites. This will lead to an understanding of the spatial distribution of both vectors and disease. An alternative, statistical approach to understanding the spatial distribution of tsetse, based on linear discriminant analysis, is illustrated with the example of Glossina morsitans in Zimbabwe, Kenya and Tanzania. In the case of Zimbabwe, a single climatic variable, the maximum of the mean monthly temperature, correctly predicts the pre-rinderpest distribution of tsetse over 82% of the country; additional climatic and vegetation variables do not improve considerably on this figure. In the cases of Kenya and Tanzania, however, another variable, the maximum of the mean monthly Normalized Difference Vegetation Index, is the single most important variable, giving correct predictions over 69% of the area; the other climatic and vegetation variables improve this to 82% overall. Such statistical analyses can guide field work towards the correct biological interpretation of the distributional limits of vectors and may also be used to make predictions about the impact of global change on vector ranges. Examples are given of the areas of Zimbabwe which would become climatically suitable for tsetse given mean temperature increases of 1, 2 and 3 degrees Centigrade. Five possible causes for sleeping sickness outbreaks are given, illustrated by the analysis of field data or from the output of mathematical models. One cause is abiotic (variation in rainfall), three are biotic (variation in vectorial potential, host immunity, or parasite virulence) and one is historical (the impact of explorers, colonizers and dictators). The implications for disease monitoring, in order to anticipate sleeping sickness outbreaks, are briefly discussed. It is concluded that present data are inadequate to distinguish between these hypotheses. The idea that sleeping sickness outbreaks are periodic (i.e. cyclical) is only barely supported by hard data. Hence it is even difficult to conclude whether the major cause of sleeping sickness outbreaks is biotic (which, in model situations, tends to produce cyclical epidemics) or abiotic.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗