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PubMedDate not supplied

The basic reproduction ratio for sexually transmitted diseases. Part 2. Effects of variable HIV infectivity.

In this paper we investigate the effects of variable infectivity on the spread of HIV in a heterosexual population where pair formation and separation are taken into account. We calculate the basic reproduction ratio as a function of the number of new partners during the infectious period, keeping the total number of contacts fixed. Numerical evidence suggests that the basic reproduction ratio decreases for variable infectivity if the average infectivity is kept constant.

Acquired Immunodeficiency Syndrome↗

PubMed1998

Components of the vectorial capacity of Aedes poicilius for Wuchereria bancrofti in Sorsogon province, Philippines.

Components of vectorial capacity (biting density, survival, and host preferences) of a population of Aedes (Finlaya) poicilius, the principal vector of Wuchereria bancrofti in the Philippines, were studied in 1994-1995 in Sorsogon province. Aedes poicilius comprised 20.7% of 3243 mosquitoes of 24 species taken in 42 nights of human-biting collections, and 1.4% of 7586 mosquitoes of 27 species taken in 18 concurrent nights of carabao-trap collections. There were, on average, 16 bites by Ae. poicilius per person per night. As there was no relationship between body size of the female Ae. poicilius and parity status, body size was not a variable affecting survivorship of Ae. poicilius. The probability of daily survival was estimated to be 0.85, and the human blood index was 0.67. None of the 862 Ae. poicilius examined contained W. bancrofti larvae, probably because of distribution of diethylcarbamazine to microfilaraemic people prior to the study. The vectorial capacity of the Ae. poicilius population under study was estimated to be 2.4 new cases per primary case per day. However, the basic reproductive rate (i.e. the number of new cases of W. bancrofti infection generated from a single infective case) was estimated to be very low because of inefficiency in parasite transmission.

Aedes↗

PubMed1995

[Contribution of a mathematical model in the control of a parasitosis: the case of human African trypanosomiasis due to Trypanosoma brucei gambiense].

Trypanosoma brucei gambiense sleeping sickness transmitted by tsetse flies (Glossina spp.) is lethal if not treated adequately. The endemicity was generally well under control in the sixties. However, since the seventies the disease is returning in most of its old foci, with alarming endemic levels in several areas. Mathematical modelling provides a rational basis for finding the optimal strategies to control these recrudescences. We present a deterministic model of the basic transmission of trypanosomiasis between human and vector hosts in natural situations. The parameters were quantified on the basis of available evidence from the literature. The model predicts a stable equilibrium state with very high prevalences: approximately 95% of humans and 27% of flies being infected. The model further shows that the build-up of an epidemic is initially very slow, and it takes several months before the equilibrium state is reached. Consequently communities have enough time to avoid catastrophic situations by migrating to safer areas. If is therefore unlikely that such high equilibrium situations will occur in practice. The expression of the basic reproductive rate R0, the number of new infections during the lifetime of an infected subject with high values of R0 implies that efforts to diminish transmission to levels where the disease cannot maintain itself in the population, have to be substantial. The necessary reduction of fly numbers in order to enable eradication, has been calculated. In almost all situations a reduction of at least 90% is necessary, which is in accordance with the field experiences of vector control programmes. The present model can be considered as a starting point in the further development of a complete simulation model, which could be applied in supporting decision making in trypanosomiasis control.

Animals↗

PubMed2006

Number of sexual encounters involving intercourse and the transmission of sexually transmitted infections.

OBJECTIVE: To investigate the impact of the number of sexual encounters involving intercourse in combination with the number of sexual partners on the transmission dynamics of sexually transmitted infections (STIs). STUDY: A statistical model is used for predicting the basic reproductive rate, R(0), which takes both the number of sexual partners and the number of sexual encounters involving intercourse per partner into consideration. The model is then applied to Swedish survey data that includes data on the number of partners over the course of 1 year, as well as the number of encounters per partner during this time. RESULTS: The number of sexual encounters involving intercourse in combination with the number of sexual partners affects the number of secondary infections in a nonlinear way. The basic reproductive rate, R(0), is lower when the heterogeneity in number of encounters is modeled than when homogeneity is assumed. CONCLUSION: The results indicate that it is possible that individuals who have a large number of partners may not, as is often assumed, be the only ones to play a central role as spreaders of STIs. Individuals who have a large number of sexual encounters involving intercourse per partner and have several (but not necessarily a very large number of) partners may also play a significant role in the transmission of STIs.

Contact Tracing↗

PubMed1994

The core group revisited: the effect of partner mixing and migration on the spread of gonorrhea, Chlamydia, and HIV.

A set of differential equations are used to model the spread of sexually transmitted diseases (STDs) in a one-sex population that includes a core group of highly sexually active subjects. The effects of partner mixing between groups and migration to and from the core on the equilibrium number of infected are shown for gonorrhea, chlamydia, and HIV. The STDs are described by the transmission probability per sexual contact and the duration of infectiousness. Partner change and intercourse frequencies are estimated from sexual survey data on heterosexual behavior. The core group is small (3% of the total population) with a partner change frequency 15 times and an intercourse frequency 2 times that of the remaining population. The degree of partner mixing and migration between the two groups can be varied. The number of sexual contacts in the three types of partnerships (core-core, "mixed," remaining population-remaining population) is also modeled. The mixed partnerships are assumed to be casual and to have a low frequency of intercourse. The model is fairly simple, and the emphasis is on qualitative rather that predictive results. The effects of partner mixing are found to be strikingly different for gonorrhea, chlamydia, and HIV. With increasing partner mixing between groups, gonorrhea shows a small increase and then a decrease in the total number of infected, whereas chlamydial infection shows a strong increase. For HIV infection the effect depends on the transmission probability; when it is 0.001 per sexual contact, the number of infected with HIV is almost unaffected by the partner mixing, and when the transmission probability is 0.002 per sexual contact, there is a strong increase in the number of HIV infected with increasing partner mixing. The effects of migration are also different for each disease. With increasing migration between groups, gonorrhea is almost unaffected in the total number of infected, whereas chlamydial infection shows a strong increase. For HIV the effect again depends on the transmission probability; when it is 0.001 per sexual contact, the number of infected with HIV shows a strong decrease, and when the transmission probability is 0.002 per sexual contact the number of HIV infected reaches its maximum for medium strong migration. A sensitivity analysis shows that for all three diseases the basic reproductive ratios (R0) and the total number of infected are sensitive to duration of infectiousness. In addition, for gonorrhea and chlamydia, RO is sensitive to the partner change rates in the core, whereas for HIV, RO is sensitive to the frequency of intercourse in the core.(ABSTRACT TRUNCATED AT 400 WORDS)

Chlamydia Infections↗

PubMed2002

A mathematical model of Staphylococcus aureus control in dairy herds.

An ordinary differential equation model was developed to simulate dynamics of Staphylococcus aureus mastitis. Data to estimate model parameters were obtained from an 18-month observational study in three commercial dairy herds. A deterministic simulation model was constructed to estimate values of the basic (R0) and effective (Rt) reproductive number in each herd, and to examine the effect of management on mastitis control. In all herds R0 was below the threshold value 1, indicating control of contagious transmission. Rt was higher than R0 because recovered individuals were more susceptible to infection than individuals without prior infection history. Disease dynamics in two herds were well described by the model. Treatment of subclinical mastitis and prevention of influx of infected individuals contributed to decrease of S. aureus prevalence. For one herd, the model failed to mimic field observations. Explanations for the discrepancy are given in a discussion of current knowledge and model assumptions.

Animal Husbandry↗

PubMed1994

Experimental quantification of vaccine-induced reduction in virus transmission.

Although reduction in transmission of an agent in the host population is an important goal of many vaccinations, suitable experimental methods to measure transmission have been lacking. Therefore, we designed and tested an animal experiment to quantify transmission among vaccinated and unvaccinated animals. We used Aujeszky's disease virus (ADV) in pigs, because a serological test was available to detect infection in vaccinated pigs and because vaccination against ADV will be used in an attempt to eliminate ADV from the Netherlands. Our experiments showed that vaccinating twice with vaccine 783 significantly reduces ADV transmission. In unvaccinated groups, the estimated maximum number of secondary cases per infectious individual, i.e. the basic reproduction ratio R0, was 10.0. In contrast, the reproduction ratio for the vaccinated groups R, i.e. the average number of secondary cases per infectious individual in a totally vaccinated population, was 0.5. These results show that it is possible to measure transmission experimentally. Therefore, such measurements should be obtained for all vaccines that are intended to eliminate agents causing animal diseases, either on a single farm or in a whole country.

Animals↗

PubMed2001

Developing stochastic epidemiological models to quantify the dynamics of infectious diseases in domestic livestock.

A stochastic model describing disease transmission dynamics for a microparasitic infection in a structured domestic animal population is developed and applied to hypothetical epidemics on a pig farm. Rational decision making regarding appropriate control strategies for infectious diseases in domestic livestock requires an understanding of the disease dynamics and risk profiles for different groups of animals. This is best achieved by means of stochastic epidemic models. Methodologies are presented for 1) estimating the probability of an epidemic, given the presence of an infected animal, whether this epidemic is major (requires intervention) or minor (dies out without intervention), and how the location of the infected animal on the farm influences the epidemic probabilities; 2) estimating the basic reproductive ratio, R0 (i.e., the expected number of secondary cases on the introduction of a single infected animal) and the variability of the estimate of this parameter; and 3) estimating the total proportion of animals infected during an epidemic and the total proportion infected at any point in time. The model can be used for assessing impact of altering farm structure on disease dynamics, as well as disease control strategies, including altering farm structure, vaccination, culling, and genetic selection.

Animals↗

PubMed2001

Utilizing stochastic genetic epidemiological models to quantify the impact of selection for resistance to infectious diseases in domestic livestock.

This paper demonstrates the use of stochastic genetic epidemiological models for quantifying the consequences of selecting animals for resistance to a microparasitic infectious disease. The model is relevant for many classes of infectious diseases where sporadic epidemics occur, and it is a powerful tool for investigating the costs, benefits, and risks associated with breeding for resistance to specific diseases. The model is parameterized for transmissible gastroenteritis, a viral disease affecting pigs, and selection for resistance to this disease on a structured pig farm is simulated. Two genetic models are used, both of which involve selection of sires. The first involves selection with the assumption of continuous genetic variation (the continuous selection model). The second involves selection with the assumption of introgression of a major recessive gene that confers resistance (the gene introgression model). In the base population, the basic reproductive ratio, R0 (i.e., the expected number of secondary cases after the introduction of a single infected animal) was 2.24, in agreement with previous studies. The probabilities of no epidemic, a minor epidemic (one that dies out without intervention), and a major epidemic were 0.55, 0.20, and 0.25, respectively. Selection for resistance, under both genetic models, resulted in a nonlinear decline in the probability of a major epidemic and a decrease in the severity of the epidemic, should it occur, until R0 was less than 1.0, at which point the probability of a major epidemic was zero. For minor epidemics, the probability and severity of the epidemic increased until R0 reached 1.0, at which point the probabilities also fell to zero. The epidemic probabilities were critically dependent on the location on the farm where infected animals were situated, and the relative risks of different groups of animals changed with selection. The main difference between the two genetic models was in the time scale; the introgression results simply depended on how quickly the resistance allele could be introgressed into the population. For the introgression model, the probability of a major epidemic declined to zero when 0.6 of the animals were homozygous for the resistance allele.

Animal Husbandry↗

PubMed1990

Population biology of pseudorabies in swine.

A deterministic mathematical model of the population biology of pseudorabies in swine was used to clarify some of the basic features of the host-virus relationship and to inquire into the circumstances that promote or impede virus persistence in a single herd. When the basic reproductive rate of the infection (ie, the number of secondary infections resulting from the introduction of a single infective animal into a wholly susceptible herd) is greater than unity, the model suggests that the number of infective individuals in the herd will undergo highly damped oscillations to a final equilibrium level. The most important determinants of virus persistence are herd size and the density at which sows are maintained. There is a threshold density of susceptible individuals below which the virus will eventually be eliminated from the herd, even when specific control measures are lacking. Test and removal strategies hasten virus elimination when herd density is already below threshold, but are otherwise likely to succeed only when the removal of latent infections reduces the basic reproductive rate of the infection below unity. Vaccination strategies may also result in virus elimination, but only in relatively small herds.

Animals↗

PubMed2005

Differential effects of reproductive and hormonal state on basic fibroblast growth factor and glial fibrillary acid protein immunoreactivity in the hypothalamus and cingulate cortex of female rats.

Morphological changes in astrocytes occur in a number of brain regions including the hypothalamus and hippocampal regions as a function of hormonal and reproductive state. Because basic fibroblast growth factor has been shown to play an important role in morphological changes in astrocytes, we investigated whether basic fibroblast growth factor immunoreactivity would also be influenced by reproductive state and circulating gonadal steroids. To do this we compared astrocytic basic fibroblast growth factor and glial fibrillary acid protein immunoreactivity in hypothalamic nuclei and the cingulate cortex, area 2 among groups of cycling, late pregnant and lactating rats as well as in ovariectomized and ovariectomized hormone-replaced females. Significant differences in both basic fibroblast growth factor and glial fibrillary acid protein immunoreactivity were observed across groups in the supraoptic nucleus, parvocellular paraventricular nucleus, medial preoptic area of the hypothalamus and cingulate cortex 2. The pattern of change in basic fibroblast growth factor and glial fibrillary acid protein immunoreactivity varied across regions both in direction and magnitude. For example, although in the supraoptic nucleus ovariectomized rats had lower levels of basic fibroblast growth factor-ir than cycling females, this pattern was reversed within cingulate cortex. Overall the results of this study suggest that reproductive and hormonal states are associated with robust changes in basic fibroblast growth factor and glial fibrillary acid protein immunoreactivity in a number of brain areas but that the changes observed vary in magnitude as well as direction from one brain region to another.

Animals↗

PubMed2001

Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios.

Two closely related stochastic models of parasitic infection are investigated: a non-linear model, where density dependent constraints are included, and a linear model appropriate to the initial behaviour of an epidemic. Host-mortality is included in both models. These models are appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In both models, the basic reproduction ratio R0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separate growth from extinction of infection. In fact we find three regions for a certain parameter where different combinations of parameters determine the behavior of the models. The proofs involve martingale and coupling methods.

Animals↗

PubMed1998

Population parameters of Triatoma spinolai (Heteroptera: Reduviidae) under different environmental conditions and densities.

Population parameters of Triatoma spinolai Porter were studied using specimens collected in the north and central region of Chile. Two cohorts of 17 and 44 first instars were maintained at a constant temperature of 28 degrees C and 70% RH. Two similar cohorts of bugs were exposed to 16-24 degrees C and 55-75% RH and maintained under a photoperiod of 14:10 (L:D) h for 16 mo. The preimaginal period ranged between 285 and 372 d under constant conditions. The lower-density cohort required 9.5 mo to reach the adult stage compared with 12.4 mo for the high-density cohort. Bugs placed under variable temperature and relative humidity conditions did not survive long. Cohorts with higher densities had similar mortality rates with greater mortality occurring in cohorts that had lower numbers of bugs. Cohorts under constant temperature and relative humidity reproduced and basic reproduction rates (Ro, intrinsic growth rate [r], and generation time [G]) were estimated. Cohorts with higher numbers of bugs had higher Ro and r, whereas values of G were similar for both groups. Apparently, 25 degrees C was a critical temperature threshold for T. spinolai and there appeared to be a minimal population density that allowed reproduction.

Animals↗

PubMed1992

Survival curves, reproductive life span and age-related pathology of Mus caroli.

Although Mus caroli is being used in a number of laboratories as an experimental animal, basic information concerning its life span, reproductive ability, and age-related pathologies has been unavailable. Here we present this basic information, and discuss the similarities to and differences from the laboratory mouse, Mus musculus domesticus [strains A/StTrWo and (A/StTrWo x C57BL/6NNia)F1] and, from published data, wild-type Mus musculus.

Aging↗

PubMed1990

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.

Age Factors↗

PubMed1981

Photosynthesis of Grass Species Differing in Carbon Dioxide Fixation Pathways : VII. CHROMOSOME NUMBERS, METAPHASE I CHROMOSOME BEHAVIOR, AND MODE OF REPRODUCTION OF PHOTOSYNTHETICALLY DISTINCT PANICUM SPECIES.

Panicum species of the Laxa group were investigated in a series of published reports and were found to possess C(4), C(3), and intermediate photosynthetic characteristics. Taxonomic and other relationships among these plants, however, are not clear. It was the objective of this investigation to document chromosome number, metaphase I chromosome behavior, and mode of reproduction, including abnormalities in the embryo sac, for these species.Chromosome counts showed a basic number (x) of 10 and ploidy levels of diploid (2n = 2x = 20), tetraploid (2n = 4x = 40), and hexaploid (2n = 6x = 60) in this group of Panicum. One diploid and one tetraploid accession of the C(4) species, Panicum prionitis Griseb., were obtained. Of the intermediate species, Panicum milioides Nees ex Trin. was diploid, Panicum schenckii Hack. was hexaploid, and Panicum decipiens Nees, ex Trin. was found to possess two ploidy levels, one accession being diploid and the other accession being hexaploid. All the C(3) species, which included two accessions of Panicum laxum Sw., three accessions of Panicum hylaeicum Mez., and one accession of Panicum rivulare Trin., were tetraploid.Meiosis was regular with primarily bivalent pairing at metaphase I in all species except the tetraploid accession of P. prionitis which possessed from 4 to 10 tetravalents. Stainable pollen was high in all species, ranging from 70 to 99%. Embryo sac analyses showed a single sac in all plants except the tetraploid accession of P. prionitis, which was found to possess an additional sac at anthesis. An additional sac was also observed in some ovaries of the P. schenckii accession. Self-pollinated seed set was high in all accessions except the diploid accession of P. prionitis and one accession of P. laxum where no seed was set under bagged conditions.This information establishes, within the limits of this collection, a base for future studies on genetic, taxonomic, photosynthetic, and evolutionary relationships among these plants. Possession of the same basic chromosome number, regular meiotic pairing, a high degree of stainable pollen, and good seed set in most of the plants studied indicate possible success in making hybrids for a genetic study of photosynthetic pathways in Panicum.

Journal Article↗

PubMed2005

Perspectives on the basic reproductive ratio.

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R0. In this paper we give a brief overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R0 from epidemiological data. Finally, we survey the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.

Animals↗

PubMed2003

Quantifying BSE control by calculating the basic reproduction ratio R0 for the infection among cattle.

The safety of using meat and bone meal (MBM) in mammal feed was studied in view of BSE, by quantifying the risk of BSE transmission through different infection routes. This risk is embodied in the basic reproduction ratio R(0) of the infection, i.e. the average number of new infections induced by one initial infection. Only when R(0) is below 1, will the disease die out with certainty and the population will become free from BSE. Unfortunately this is a slow process due to the slow progression of the disease. We calculate R(0) explicitly from basic ingredients taking several different transmission routes into account. Several of the basic ingredients are functions of age or of infection-age. We also calculate the exponential growth rate r in terms of the same basic ingredients. Next we quantify the ingredients from available data and compute the effects on R(0) of various scenario's for controlling BSE, with examples for the UK and the Netherlands.

Age Factors↗