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Results for “Basic Reproduction Number”

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PubMedDate not supplied

Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression.

Mathematical analysis is carried out that completely determines the global dynamics of a mathematical model for the transmission of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). HTLV-I infection of healthy CD4(+) T cells takes place through cell-to-cell contact with infected T cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. Our analysis establishes that the global dynamics of T cells are completely determined by a basic reproduction number R(0). If R(0)< or =1, infected T cells always die out. If R(0)>1, HTLV-I infection becomes chronic, and a unique endemic equilibrium is globally stable in the interior of the feasible region. We also show that the equilibrium level of ATL-cell proliferation is higher when the HTLV-I infection of T cells is chronic than when it is acute.

Adult↗

PubMedDate not supplied

Daniel Bernoulli's epidemiological model revisited.

The seminal paper by Daniel Bernoulli published in 1766 is put into a new perspective. After a short account of smallpox inoculation and of Bernoulli's life, the motivation for that paper and its impact are described. It determines the age-specific equilibrium prevalence of immune individuals in an endemic potentially lethal infectious disease. The gain in life expectancy after elimination of this cause of death can be explicitly expressed in terms of the case fatality and the endemic prevalence of susceptibles. D'Alembert developed in 1761 an alternative method for dealing with competing risks of death, which is also applicable to non-infectious diseases. Bernoulli's formula for the endemic prevalence of susceptibles has so far escaped attention. It involves the lifetime risk of the infection, the force of infection and the life expectancy at birth. A new formula for the basic reproduction number is derived which involves the average force of infection, the average case fatality and the life expectancy at the time of infection. One can use this estimate to assess the gain in life expectancy if only a fraction of the population is immunized.

Age Factors↗

PubMed2003

A qualitative analysis of a model for the transmission of varicella-zoster virus.

Varicella-zoster virus (VZV) is a herpesvirus which is the known agent for causing varicella (chickenpox) in its initial manifestation and zoster (shingles) in a reactivated state. The standard SEIR compartmental model is modified to include the cycle of shingles acquisition, recovery, and possible reacquisition. The basic reproduction number R(0) shows the influence of the zoster cycle and how shingles can be important in maintaining VZV in populations. The model has the typical threshold behavior in the sense that when R(0)</=1, the VZV disappears from the population, and when R(0)>1, the virus persists over time and so chickenpox and shingles remain endemic.

Chickenpox↗

PubMed1998

Global stability of an age-structure model for TB and its applications to optimal vaccination strategies.

This article focuses on the study of an age-structure model for the disease transmission dynamics of tuberculosis in populations that are subjected to a vaccination program. We first show that the infection-free steady state is globally stable if the basic reproductive number R0 is below one, and that an endemic steady state exists when the reproductive number in the presence of vaccine is above one. We then apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategies can be either one- or two-age strategies.

Age Distribution↗

PubMed2000

Comparison of deterministic and stochastic SIS and SIR models in discrete time.

The dynamics of deterministic and stochastic discrete-time epidemic models are analyzed and compared. The discrete-time stochastic models are Markov chains, approximations to the continuous-time models. Models of SIS and SIR type with constant population size and general force of infection are analyzed, then a more general SIS model with variable population size is analyzed. In the deterministic models, the value of the basic reproductive number R0 determines persistence or extinction of the disease. If R0 < 1, the disease is eliminated, whereas if R0 > 1, the disease persists in the population. Since all stochastic models considered in this paper have finite state spaces with at least one absorbing state, ultimate disease extinction is certain regardless of the value of R0. However, in some cases, the time until disease extinction may be very long. In these cases, if the probability distribution is conditioned on non-extinction, then when R0 > 1, there exists a quasi-stationary probability distribution whose mean agrees with deterministic endemic equilibrium. The expected duration of the epidemic is investigated numerically.

Disease Outbreaks↗

PubMedDate not supplied

The risk of yellow fever in a dengue-infested area.

Yellow fever and dengue are viral infections that in urban centres are transmitted by the same arthropod vector, a mosquito of the genus Aedes. In order to estimate the risk of an epidemic of urban yellow fever in a dengue-infested area we calculated the threshold in the basic reproduction number, R0, of dengue, above which any single sylvatic yellow fever-infected individual will trigger an urban yellow fever epidemic. Specifically, we analysed the relationship between the extrinsic incubation period and the duration of viraemia, from which it is possible to define the R0 for dengue that would also suggest an outbreak potential for yellow fever. We also calculated the critical proportion of people to vaccinate against yellow fever in order to prevent an epidemic in a dengue-endemic area. The theory proposed is illustrated by the case of São Paulo State in southern Brazil, where dengue is endemic and the risk of urban yellow fever is already imminent.

Aedes↗

PubMedDate not supplied

The effect of mass administration of sulfadoxine-pyrimethamine combined with artesunate on malaria incidence: a double-blind, community-randomized, placebo-controlled trial in The Gambia.

A double-blind, community-randomized, placebo-controlled trial was conducted in a rural area of The Gambia between June and December 1999 to test whether a reduction in the infectious reservoir can reduce malaria transmission. Overall 14,017 (85%) individuals living in the study area were treated with either placebo or sulfadoxine-pyrimethamine (SP) combined with a single dose of artesunate (AS). Following the mass drug administration (MDA) 1375 children aged 6 months to 10 years were kept under surveillance for clinical malaria in 18 villages throughout the 1999 malaria transmission season. During a 20-week surveillance period 637 episodes of malaria were detected. The mean incidence rate was 2.5/100 child-weeks in the placebo villages, and 2.3/100 child-weeks in villages that received SP + AS. The mean rate ratio, adjusted for individual and village-level covariates, was 0.91 (95% CI 0.68-1.22, P = 0.49). During the first 2 months of surveillance, the malaria incidence was lower in treated villages. After 2 months the incidence was slightly higher in the MDA group but this was not statistically significant. Overall, no benefit of the MDA could be detected. The reason for the absence of an impact on malaria transmission is probably the very high basic reproductive number of malaria, and the persistence of mature gametocytes, which are not affected by AS treatment.

Adult↗

PubMed2001

Encouraging prospects for immunisation against primary cytomegalovirus infection.

Congenital cytomegalovirus (CMV) infection is the leading infectious cause of mental retardation in children. Using seroprevalence data from two large antenatal populations (in excess of 14000 women) coupled with a mathematical modelling approach, we have shown that CMV has a low force of infection (ca. 0.03 per seronegative per annum) and its basic reproductive number R0 is relatively modest at 2.4. On the basis of these results, the critical vaccination proportion required for eradication of CMV is between 59-62%. In contrast to the predicted and observed effects of rubella vaccination on the incidence of congenital rubella, the increase in the average age of infection following instigation of a CMV vaccine programme will not increase the number of congenital infections. In conclusion, CMV is a prime candidate for eradication from the human population through vaccination.

Adult↗

PubMed1999

Epidemiological patterns of canine leishmaniasis [correction of leishmaniosis] in Western Liguria (Italy).

An epidemiological survey was carried out on the distribution of canine leishmaniasis in Western Liguria (Northern Italy). Blood sera from 21146 dogs collected from 1990 to 1996 were subjected to the indirect immunofluorescence test (IFAT). From 1990 to 1994 (16690 dogs), only monthly seroprevalences were calculated (min 14%-max 60.5%). Dog sera sampled from October 1994 to May 1996 (4456 dogs) were divided into two subgroups (I: October 1994-May 1995; II: October 1995-May 1996). Seroprevalence was 30.3% and 22.1% in these two groups, respectively. Data analysis by log-linear models revealed that serological positivity to Leishmania sp. was significantly associated with a dog's outdoor lifestyle, with a rural environment and with the male sex. Of the 218 dogs which were tested twice seroconversion rates were also higher in outdoor, rural and male dogs while negativization rates were lower in the same groups. Basic reproductive numbers (R0) were 1.53 (subgroup I) and 1.28 (subgroup II).

Animals↗

PubMed1997

The design of veterinary vaccination programmes.

The optimal design of a veterinary vaccination programme depends on both the characteristics of the vaccine and the epidemiology of the pathogen or parasite. Relevant vaccine characteristics are the proportion of those vaccinated that are initially protected, the duration of protection and the coverage achieved by the vaccination programme. The most important epidemiological parameter is the basic reproduction number, R0. Mathematical theory can integrate this information to address such questions as: whether it is possible to eliminate an infection; what proportion of hosts must be vaccinated to achieve this: what age should hosts first be vaccinated; and at what interval should hosts be revaccinated? Examples of rabies in foxes and foot-and-mouth disease in cattle suggest that theory can be used to guide the design of vaccination programmes.

Animals↗

PubMed2002

Could widespread use of combination antiretroviral therapy eradicate HIV epidemics?

Current combination antiretroviral therapies (ARV) are widely used to treat HIV. However drug-resistant strains of HIV have quickly evolved, and the level of risky behaviour has increased in certain communities. Hence, currently the overall impact that ARV will have on HIV epidemics remains unclear. We have used a mathematical model to predict whether the current therapies: are reducing the severity of HIV epidemics, and could even lead to eradication of a high-prevalence (30%) epidemic. We quantified the epidemic-level impact of ARV on reducing epidemic severity by deriving the basic reproduction number (R(0)(ARV)). R(0)(ARV) specifies the average number of new infections that one HIV case generates during his lifetime when ARV is available and ARV-resistant strains can evolve and be transmitted; if R(0)(ARV) is less than one epidemic eradication is possible. We estimated for the HIV epidemic in the San Francisco gay community (using uncertainty analysis), the present day value of R(0)(ARV), and the probability of epidemic eradication. We assumed a high usage of ARV and three behavioural assumptions: that risky sex would (1) decrease, (2) remain stable, or (3) increase. Our estimated values of R(0)(ARV) (median and interquartile range [IQR]) were: 0.90 (0.85-0.96) if risky sex decreases, 1.0 (0.94-1.05) if risky sex remains stable, and 1.16 (1.05-1.28) if risky sex increases. R(0)(ARV) decreased as the fraction of cases receiving treatment increased. The probability of epidemic eradication is high (p=0.85) if risky sex decreases, moderate (p=0.5) if levels of risky sex remain stable, and low (p=0.13) if risky sex increases. We conclude that ARV can function as an effective HIV-prevention tool, even with high levels of drug resistance and risky sex. Furthermore, even a high-prevalence HIV epidemic could be eradicated using current ARV.

Anti-HIV Agents↗

PubMed2002

Threshold conditions for infection persistence in complex host-vectors interactions.

As classically defined by Macdonald in the early 1950s, for the case of diseases with one vector and one host, the Basic Reproduction Number, R0, is defined as the number of secondary infections caused by a single infective of the same type (vector or host) during its infectiousness period in an entirely susceptible population. In the case of a disease which has one vector and one host, it is easy to show that R0 coincides with the threshold for the establishment of an endemic state: if R0 > 1 (< 1), the disease can invade (cannot invade) the host population. In this paper we examine various epidemic situations in which there are more than one vector and/or host. We show that in those more complex systems it is not possible to deduce a single R0 but rather a threshold for infection persistence which is a composite of several quantities closely related to the classical expression of R0. Another definition of R0 given by Diekmann, Heesterbeek and Metz, and denoted in this paper R0NGO is discussed and applied as an alternative to calculate the thresholds for infection establishment.

Animals↗

PubMed2006

Domestic dogs and cats as sources of Trypanosoma cruzi infection in rural northwestern Argentina.

The reservoir capacity of domestic cats and dogs for Trypanosoma cruzi infection and the host-feeding patterns of domestic Triatoma infestans were assessed longitudinally in 2 infested rural villages in north-western Argentina. A total of 86 dogs and 38 cats was repeatedly examined for T. cruzi infection by serology and/or xenodiagnosis. The composite prevalence of infection in dogs (60%), but not in cats, increased significantly with age and with the domiciliary density of infected T. infestans. Dogs and cats had similarly high forces of infection, prevalence of infectious hosts (41-42%), and infectiousness to bugs at a wide range of infected bug densities. The infectiousness to bugs of seropositive dogs declined significantly with increasing dog age and was highly aggregated. Individual dog infectiousness to bugs was significantly autocorrelated over time. Domestic T. infestans fed on dogs showed higher infection prevalence (49%) than those fed on cats (39%), humans (38%) or chickens (29%) among 1085 bugs examined. The basic reproduction number of T. cruzi in dogs was at least 8.2. Both cats and dogs are epidemiologically important sources of infection for bugs and householders, dogs nearly 3 times more than cats.

Age Factors↗

PubMed1998

Heterogeneities in schistosome transmission dynamics and control.

We review the theoretical framework for exploring the impact of individual and spatial heterogeneities in patterns of exposure and contamination and on the basic reproduction number, R0, for human schistosomes. Analysis of water contact data for 5 communities in Zimbabwe and Mali suggests that the impact is substantial, increasing R0 by factors of up to 6.5, mostly due to highly overdispersed distributions of contact rates among individuals. Several practical conclusions emerge: concentration of contacts at a single site should be avoided; the impact of control targeted at certain sites cannot be predicted without knowledge of how individuals' contacts are distributed among sites; control programmes targeted at individuals or sites contributing most to transmission can be very efficient but, conversely, will be ineffective if any of these individuals or sites are missed.

Animals↗

PubMed2000

Predictions of the emergence of vaccine-resistant hepatitis B in The Gambia using a mathematical model.

Vaccine escape variants of hepatitis B virus (HBV) have been identified world-wide. A mathematical model of HBV transmission is used to investigate the potential pattern of emergence of such variants. Attention is focused on The Gambia as a country with high quality epidemiological data, universal infant immunization and in which escape mutants after childhood infections have been observed. We predict that a variant cannot become dominant for at least 20 years from the start of vaccination, even when using a vaccine which affords no cross protection. The dominant factor responsible for this long time scale is the low rate of infectious contacts between infected and susceptible individuals (we estimate the basic reproduction number of hepatitis B in The Gambia to be 1.7). A variant strain that achieves high prevalence will also take many years to control, and it is questionable whether emergence will be identifiable by sero-surveillance until of high prevalence. The sensitivity of the model predictions to epidemiological and demographic factors is explored.

Adolescent↗

PubMed1996

Failure of vaccination to prevent outbreaks of foot-and-mouth disease.

Outbreaks of foot-and-mouth disease persist in dairy cattle herds in Saudi Arabia despite revaccination at intervals of 4-6 months. Vaccine trials provide data on antibody responses following vaccination. Using this information we developed a mathematical model of the decay of protective antibodies with which we estimated the fraction of susceptible animals at a given time after vaccination. The model describes the data well, suggesting over 95% take with an antibody half-life of 43 days. Farm records provided data on the time course of five outbreaks. We applied a 'SLIR' epidemiological model to these data, fitting a single parameter representing disease transmission rate. The analysis provides estimates of the basic reproduction number R(0), which may exceed 70 in some cases. We conclude that the critical intervaccination interval which would provide herd immunity against FMDV is unrealistically short, especially for heterologous challenge. We suggest that it may not be possible to prevent foot-and-mouth disease outbreaks on these farms using currently available vaccines.

Animals↗

PubMed2001

Persistence patterns of scrapie in a sheep flock.

The epidemiology and transmission dynamics of sheep scrapie is as yet poorly understood. Here we present a theoretical analysis of the transmission dynamics within a sheep flock, concentrating on how persistence properties depend on transmission scenario and flock size. Patterns of disease persistence and extinction are studied analytically using branching-process approximations and numerically using stochastic model simulations. For a given basic reproduction number, disease extinction is most likely when late-stage infected animals are responsible for most of the transmission. This effect can be understood in terms of aggregation in the distribution of the number of secondary infections arising from a single primary infection. The presence of an environmental reservoir reduces the probability of extinction.

Animals↗

PubMed2002

Vaccination against hepatitis B in low endemic countries.

A mathematical model that takes transmission by sexual contact and vertical transmission into account was employed to describe the transmission dynamics of hepatitis B virus (HBV) and vaccination against it. The model is an extension of a model by Williams et al. (Epidemiol Infect 1996: 116; 71-89) in that it takes immigration of hepatitis B carriers from countries with higher prevalence into account. Model parameters were estimated from data from The Netherlands where available. The main results were that, given the estimates for the parameters describing sexual behaviour in The Netherlands, the basic reproduction number R0 is smaller than 1 in the heterosexual population. As a consequence, the immigration of carriers into the population largely determines the prevalence of HBV carriage and therefore limits the possible success of universal vaccination. Taking into account the prevalence of hepatitis B carriage among immigrants and an age-dependent probability of becoming a carrier after infection, we estimate that a fraction of between 5 and 10% of carrier states could be prevented by universal vaccination.

Adolescent↗