The risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA

We estimate the risk of acquiring the new influenza A(H1N1) for Brazilian travelers to Chile, Argentina and the USA. This is done by a mathematical model that quantifies the intensity of transmission of the new virus in those countries and the probability that one individual has of acquiring the influenza depending on the date of arrival and time spent in the area. The maximum estimated risk reached 7.5 cases per 10,000 visitors to Chile, 17 cases per 10,000 travelers to Argentina and 23 cases per 10,000 travelers to the USA. The estimated number of imported cases until 27 July is 57 +/- 9 from Chile, 136 +/- 27 from the USA and 301 +/- 21 from Argentina, which are in accord with the official figures. Estimating the number of imported cases was particularly important for the moment of the disease introduction into this country, but it will certainly be important again as a tool to calculate the number of future imported cases from northern countries in our next inter-epidemic season, were imported cases can constitute again the majority of the new influenza burden to the Brazilian health services.

A mixed ectoparasite--microparasite model for bat-transmitted rabies

This paper considers the transmission of rabies to domestic livestock by vampire bats. Vampire bats act as ectoparasites on cattle both by ingesting a small amount of blood every night and by prolonging bleeding by the action of anticoagulant substances in their saliva. In addition to this parasitic action bats may also transmit rabies, inflicting important losses on affected herds by the inevitable mortality due to the infection. We modeled this complex interaction and we also demonstrate that bat control measures are more effective in reducing rabies prevalence and mortality by rabies than cattle vaccination.

Modelling the natural history of HIV infection in individuals and its epidemiological implications

The variation of viraemia in the natural course of HIV infection is expected to have major influence on the probability of transmission and, consequently, on the epidemiology of HIV/AIDS. In this paper we propose a model which takes into account the time evolution of HIV viraemia (measured as HIV-RNA copies per ml of blood) in an infected individual and its impact on the threshold for the establishment of an endemic level, and mainly on the relative contribution of each of the clinical phases of the infection to the total transmission of HIV per infected individual. We consider that an infected individual passes through three phases of viraemia. The first phase, which lasts for 6-7 weeks, is characterized by very high viraemia. In the second phase, which lasts about 10 years, the viraemia is much lower, increasing again in the last phase, which lasts up to two years, and ends in full-blown AIDS. We show that the relative contribution of each phase to the total transmission of HIV is very sensitive to the model we assume for the dependence of the transmissibility of HIV on the viral load. For instance, if we assume that transmissibility is proportional to the decimal logarithm of viraemia, then the second phase predominates always. Due to the epidemiological importance of this fact, it is clear that further improvement on virological research to better understand the dependence of HIV transmissibility on the viral concentration in biological fluids is necessary.

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.

On the uniqueness of the positive solution of an integral equation which appears in epidemiological models

In this paper, we show that the positive solution of a nonlinear integral equation which appears in classical SIR epidemiological models is unique. The demonstration of this fact is necessary to justify the correctness of any approximate or numerical solution. The SIR epidemiological model is used only for simplicity. In fact, the methods used can be easily extended to prove the existence and uniqueness of the more involved integral equations that appear when more biological realities are considered. Thus the inclusion of a latent class (SLIR models) and models incorporating variability in the infectiousness with duration of the infection and spatial distribution lead to integral equations to which the results derived in this paper apply immediately.

Acquired immunity of a schistosomiasis transmission model--analysis of the stabilizing effects

A semi-stochastic model for schistosomiasis was developed based on the immune response built up by human host after elapsing a fixed period of time L from the first infection, and on the parasite infection with multiple occurrences. Both acquired immunity and multiple parasite infections reproduced a great endemic stability for the disease and a high value for the basic reproduction ratio.

Acquired immunity on a schistosomiasis transmission model - fitting the data

A semi-stochastic model is proposed to analyse the effects of acquired immunity on the transmission of schistosomiasis in the human host. The basic model's assumptions are as follows. The human host is assumed to build up an immune response after elapsing a fixed period of time L from the first infection. This acquired immunity is assumed to be partially effective and it is never lost. The parasite infection event is a Poisson process with multiple occurrences, i.e., in each event one or more cercaria are assumed to invade the host. The model treats deterministically the age distribution of human host. The model shows a good retrieving capacity of real data from two endemic areas of schistosomiasis: Touros, Brazil (Schistosoma mansoni) and Misungwi, Tanzania (Schistosoma haematobium).

Assessing the efficacy of a mixed vaccination strategy against rubella in São Paulo, Brazil

BACKGROUND

In 1992 a major vaccination strategy against measles-mumps-rubella was introduced in the State of Saão Paulo, Brazil. This strategy was based on mathematical models and comprised a pulse vaccination covering all children aged 1-10 years, followed by the inclusion of this vaccine in the routine calendar at 15 months of age. The present work reports the evaluation of the efficacy of this mixed vaccination strategy.

METHODS

A rubella seroprevalence survey was carried out immediately and one year after the campaign, comprising 4953 children aged 1-15 years.

RESULTS

We show that average rubella seroprevalence increased from 0.40 to 0.97 and that the reported number of congenital rubella syndrome (CRS) cases dropped dramatically.

CONCLUSIONS

The mixed vaccination strategy adopted against rubella has proved to be very effective in reducing the number of CRS cases in São Paulo.

The basic reproduction ratio of HIV among intravenous drug users

A new approach for the estimation of the Basic Reproduction Ratio R0 for HIV among intravenous drug users (IVDU) is proposed. This approach is based in an adaptation of the models proposed by Ross and Macdonald for vector-borne infections. A straightforward adaptation of Macdonald's model is presented first: biological vectors are replaced by needles and syringes and we consider a homogeneous population of IVDUs; next we present a modified model where several heterogeneities are considered. Some of those heterogeneities are due to intrinsic differences between needles and syringes and biological vectors; others, such as those related to movements of individuals between communities, should apply to both biological vectors and injection apparatuses. An example of the calculations of R0 for a real IVDUs community is presented.

A model-based design of a vaccination strategy against rubella in a non-immunized community of São Paulo State, Brazil

A mixed vaccination strategy against rubella is proposed. We describe how the vaccination strategy was designed with the help of mathematical techniques. The strategy was designed for application in a non-immunized community of the State of São Paulo, Brazil, and was implemented by local health authorities in 1992. This strategy comprises a pulse vaccination campaign, covering the age interval between 1 and 10 years, followed by the introduction of the vaccine in the immunization calendar at 15 months of age. The expected impact of the proposed strategy is discussed.

Malaria prevalence amongst Brazilian Indians assessed by a new mathematical model

An alternative way to estimate the endemic level of malaria amongst Brazilian indians is proposed. This is achieved by estimating the age-related 'force of infection' of malaria (the effective inoculation rate), applying a mathematical model, described elsewhere, to serological data. In addition we present a way to estimate the Basic Reproductive Rate of malaria in the same area. The results have shown a good degree of accuracy in describing the endemic pattern of malaria in the area, and also indicate some relevant aspects of its age distribution related to the design of control strategies.

Malaria transmission rates estimated from serological data

A mathematical model was used to estimate malaria transmission rates based on serological data. The model is minimally stochastic and assumes an age-dependent force of infection for malaria. The transmission rates estimated were applied to a simple compartmental model in order to mimic the malaria transmission. The model has shown a good retrieving capacity for serological and parasite prevalence data.

Effects of vaccination programmes on transmission rates of infections and related threshold conditions for control

This study addresses the problem of the existence of conditions for persistence or eradication of age-dependent directly transmitted infections. The usual system of differential equations describing the dynamics of the disease is transformed into integral equations. The authors show how to solve these equations and, by applying the contraction mapping theorem, give conditions for the persistence or eradication of the infection. A practical illustration of the application of the methods proposed is sketched, using data for rubella collected from a small Brazilian community.

A model of schistosomiasis incorporating the searching capacity of the miracidium

This paper describes a modification of the model for the transmission of schistosomiasis proposed by Macdonald (1965), which allows the snail host-locating efficiency of the miracidium to be taken into account. The modified model allows for a choice of miracidia efficiency. If it is assumed that the miracidia are inefficient hunters than the resulting model is very sensitive to perturbations; relatively small changes in small numbers not only cause appreciable changes in the percentage of snails infected but resulted in attainment of the threshold (the point at which schistosomiasis ceases to be endemic). If, however, the miracidia are efficient snail hunters then the model is much less sensitive to perturbations; here the percentage of snails infected is much less affected by changing snail numbers, and the threshold is much more difficult to reach by reducing snail numbers. It is argued that, on the whole, the empirical data give more support to the latter model, although there are some circumstances under which the former model might apply. However, even with these modifications it is considered that the Macdonald model does not provide a satisfactory explantation of field observations.