Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Effect of continuous growing of resistant soybean genotypes on Meloidogyne arenaria race 1 reproduction

Even though resistance is the most promising tactic for root-knot nematode management on soybean (Glycine max), virulent biotypes may occur and be selected on specific resistant plant genotypes. In the present study, reproduction rate of Meloidogyne arenaria race 1 increased after four sequences of continuous culture of the parasite on resistant soybean genotypes.

Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)

OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil

OBJECTIVE: To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengue-infested area. METHODS: The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS: In this study the analysis was expanded to the epidemiological situation of dengue in São Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS: Currently there is a great number of non-vaccinated people living in Aedes aegypti infested area in the state of São Paulo.

Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil

OBJECTIVE: To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS: The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R0 of imported versus autochthonous cases was used as an estimator of real R0. RESULTS: The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R0 above one, although the real R0 was below one. The same results were seen when the method was applied on simulated epidemics with fixed R0. This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R0 values. CONCLUSIONS: It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease.

Vital Statistics of Panstrongylus geniculatus (Latreille 1811) (Hemiptera: Reduviidae) under Experimental Conditions

A statistical evaluation of the population dynamics of Panstrongylus geniculatus is based on a cohort experiment conducted under controlled laboratory conditions. Animals were fed on hen every 15 days. Egg incubation took 21 days; mean duration of 1st, 2nd, 3rd, 4th, and 5th instar nymphs was 25, 30, 58, 62, and 67 days, respectively; mean nymphal development time was 39 weeks and adult longevity was 72 weeks. Females reproduced during 30 weeks, producing an average of 61.6 eggs for female on its lifetime; the average number of eggs/female/week was 2.1. Total number of eggs produced by the cohort was 1379. Average hatch for the cohort was 88.9%; it was not affected by age of the mother. Age specific survival and reproduction tables were constructed. The following population parameters were evaluated, generation time was 36.1 weeks; net reproduction rate was 89.4; intrinsic rate of natural increase was 0.125; instantaneous birth and death rates were 0.163 and 0.039 respectively; finite rate of increase was 1.13; total reproductive value was 1196 and stable age distribution was 31.2% eggs, 64.7% nymphs and 4.1% adults. Finally the population characteristics of P. geniculatus lead to the conclusion that this species is a K strategist.

Dynamics of the 2006/2007 dengue outbreak in Brazil

We analyzed dengue incidence in the period between October 2006-July 2007 of 146 cities around the country were Larval Index Rapid Assay (LIRA) surveillance was carried out in October 2006. Of these, we chosen 61 cities that had 500 or more cases reported during this period. We calculated the incidence coefficient, the force of infection (») and the basic reproduction number (R0) of dengue in those 61 cities and correlated those variables with the LIRA. We concluded that » and R0 are more associated with the number of cases than LIRA. In addition, the average R0 for the 2006/2007 dengue season was almost as high as that calculated for the 2001/2002 season, the worst in Brazilian history.

Tabela de vida de fertilidade de Lysiphlebus testaceipes (Cresson, 1880) (Hymenoptera, Aphidiidae) em Schizaphis graminum (Rondani, 1852) (Hemipera, Aphididae)

Life table analyses have been developed to understanding the impact of various sources of intrinsic and extrinsic mortalities on the rate of population growth. The understanding of the population increase of the parasitoids related to their hosts is important in biological control programs. This work had as objective to evaluate the survival and fertility of the parasitoid Lysiphlebus testaceipes (Cresson, 1880) on Schizaphis graminum (Rondani, 1852) as a host under fertility life table. The experiment were carried out in a climatic chamber at 25 ± 1ºC, RH 60 ± 10% and 10h photophase. To determine the immature mortality, the development time and the sex ratio of the parasitoid, 12 females of the parasitoid (less than one day old) and 240 nymphs of S. graminum (3 days old) were used. To evaluate the longevity and fertility of L. testaceipes, 15 females (less than one day old) were used. Nymphs of S. graminum (3 days old) were offered for each parasitoid female daily, until the female died, being in the 1st day - 300 nymphs; 2nd day - 250 nymphs; 3rd day - 200 nymphs; 4th day - 150 and in the other days a number of 50 nymphs. L. testaceipes had an immature mortality of 22,2%, and a development time of males and females of 9.0 and 9.1 days, respectively. The females of L. testaceipes laid, in it first life day, 257.8 eggs, and they survived up until seven days. The net reproduction rate (Ro) and the intrinsic rate of increase (r m) were respectively, 301.9 and 0.513. The finite rate of increase (l) was 1.67 females per day, the mean length of a generation (T) was 11.13 days and the time to duplicate the population (TD) was 1.35 weeks. The parasitoid L. testaceipes have a high potential of population growth on S. graminum as a host under the analyzed conditions.

Metas para inflação e taxa de juros no Brasil: uma análise do efeito dos preços livres e administrados

After surpassed more than half a decade since the adoption of inflation targeting in Brazil, it can be seen that maintaining a high interest rate is inherent to the strategy for the conduction of the monetary policy. The objective of this paper is to show that the present policy for defining the basic interest rate of the economy, based on the response to inflation considering both market and administered prices, is onerous for the Brazilian society. Based on findings from empirical evidence in the period 1999-2004, the adoption of a core inflation, a change in the time horizon for definition of targets, and, in common agreement between Banco Central do Brasil and National Treasury, a definition of these inflation targets, as a framework to increase efficiency of the monetary regime, creates possibilities for proposing a reduction on the Selic rate.

Convenções financeiras e a taxa básica de juros no Brasil: uma primeira aproximação

Financial conventions and basic interest rate in Brazil. This article discusses the thesis that the Brazilian interest rate is a convention, focusing on the basic interest rate under the inflation targeting regime. On the one hand, there are some complications involved in this debate. In order to show this, we consider the theoretical works that have been references for the Brazilian economists who see an interest rate convention in the country. On the other hand, despite the difficulties, it is possible to find signs of conventionality in the determination of the Brazilian basic rate, by analyzing two properties of conventions: conformity of some with the conformity of others; and arbitrariness.

Production of basic potato seed minitubers in substrate and different nitrogen rates

The optimal dose of nitrogen (N) in potato crop depends on the production system. The objective of this study was to determine the optimal dose of N for the production of basic potato seed minitubers and evaluate the effect of N rates on physiological and nitrogen indices in the youngest fully developed leaf (fourth leaf) and in the oldest leaf of the plants at 60 days after planting. The experiment was conducted in a greenhouse at the Departamento de Fitotecnia da Universidade Federal de Viçosa. The treatments consisted of five N rates (0, 45, 90, 180 and 360 mg dm-3), with 10% of each dose applied at planting and the remainder through irrigation water, daily, for 30 days. The nitrogen rates positively influenced the physiological indices (length, width, leaf area, number of leaves, fresh mass and dry mass) and nitrogen (level and content of N and N-NO³ in the dry mass and SPAD) both in the fourth leaf and in the oldest leaf. Likewise, the N rates positively influenced the number and mass of harvested tubers. The largest number (5.44 tubers/plant) and the maximum mass of tubers (243.5 g/plant) were obtained with 360.0 and 332.9 mg N dm-3, respectively. Therefore, the mass and number of tubers were not optimized by the same N rate. The critical SPAD index was 38.8 in the fourth leaf, which was more sensitive to the effect of N rates than the oldest leaf.

Fecundity of the spider crab Mithraculus forceps (Decapoda, Mithracidae) from the northeastern coast of the state of São Paulo, Brazil

Fecundity is one of the most important parameters in studying the reproductive output of Pleocyemata decapods, especially because of its relationship to the efficiency of population replacement. Knowledge of fecundity provides basic elements for understanding the reproductive strategies, dynamics, and evolution of a given population. The present investigation provides informations on fecundity, egg size, egg loss, and the relationship between fecundity and selected environmental features, for the spider crab Mithraculus forceps (A. Milne Edwards, 1875). Ovigerous crabs were collected each month during 2000, by SCUBA diving, at Couves Island (23º25'25"S, 44º52'03"W) on the northeastern coast of the state of São Paulo, Brazil. A total of 40 ovigerous females with egg in early development (initial stage) and 28 final stage eggs were obtained and analyzed. Mean fecundity, from eggs of the initial stage, was 402.8 ± 240.1 eggs, ranging from 60 to 1,123 eggs. Sizes of females ranged from 9.4 to 14.0 mm carapace width. Mean egg size was 0.56 ± 0.06 mm diameter. A 20.33% rate of egg loss was estimated by comparing the fecundities of batches of eggs in early and late development (40 initial batches and 28 final stages batches). There were no significant relationships between the water temperature or salinity and variations in fecundity. As in most brachyuran species, M. forceps showed a strong conservative relationship between fecundity and body size.

Differences on allocation of available resources, in growth, reproduction, and survival, in an exotic gastropod of Physidae compared to an endemic one

Physa acuta Draparnaud, 1805 is an invasive gastropod that can affect local species. In Argentina, it is widespread and abundant, even in environments inhabited by the native species Stenophysa marmorata Guilding, 1828. Its predominance raises the question whether this could be explained by a more successful energy allocation in functional requirements (growth, reproduction and survival) compared to S. marmorata. This study was aimed at comparing growth rates, as well as survival and fecundity, between both species under laboratory conditions. Individuals born on the same day were grouped in four per aquaria and kept under controlled conditions of food, light, and temperature. Snails were weekly measured (maximum shell length), and growth rates were calculated using the Von Bertalanffy's equation. The number of eggs and survivors were grouped by week. Stenophysa marmorata was larger at birth than Physa acuta and invested more energy in growth, delaying sexual maturity. This resulted in a disadvantage in fecundity and survival compared to P. acuta, which had a lower growth rate but matured earlier and survived longer. Furthermore, the growth of P. acuta was not affected by reproduction, its reproductive period was longer, consequently with more eggs laid than S. marmorata.

Features of reproduction in laboratory-reared Aedes fluviatilis (Lutz, 1904) (Diptera: Culicidae)

Observations were made on 100 female Aedes fluviatilis (Lutz) maintained individually from the first blood meal onwards and allowed one blood meal during each oviposition cycle, 5% dextrose solution been supplied throughout life. The average length of live was 49.9 ± 17.8 days; the logarithm of the mortality rate increased proportionately to physiological age. The insects took an average of 7.3 ± 3.2 blood meals and produced a mean of 7.9 ± 3.7 clutches of eggs. There was a progressive decrease, proportional to advancing physiological age, in the mean numbers of eggs laid in successive oviposition cycles, in the intervals between blood feeding oviposition, and in the numbers of larvae that hatched. Delayed oviposition, transient sterility and a total loss of fertility were also recorded.

The Influence of Self-fertilization performance and Copulation Behaviour in Reproduction by Cross-fertilization in Groups of Biomphalaria tenagophila (Mollusca, Planorbidae)

The following hypotheses were tested for groups of simultaneous hermaphrodites Biomphalaria tenagophila: (a) snails that have low reproductive success during the process of self-fertilization do not increase their reproductive success after the end of grouping; (b) the copulation behaviour and the presence of one snail whose eggs have a low viability rate influence the partner's reproductive success by cross-fertilization. Groups were constituted by a homozygous pigmented snail and two albinos: one with a viability rate higher than 70% ("good reproducers") and the other less than 10% ("bad reproducers"). All pigmented snails had viability rates higher than 70%. The "good" and "bad" reproducer albino snails had similar copulation behaviour. However, after the end of grouping, the "bad reproducers" continued to have viability rates less than 10% over 30 days. In 100% of the cases that pigmented snails copulated (performing either a male role or simultaneously male and female roles) exclusively with "good" reproducer albinos, they presented high reproductive success (producing, on average of 8.4 pigmented embryos/egg-mass). However, in 100% of the cases that pigmented snails copulated with both partners, the "good" reproducer albino snails produced none or very few embryos (the highest average was 2.2 pigmented embryos/egg-mass). Therefore, the production of viable embryos by cross-fertilization was more influenced by self-fertilization performance than by copulation behaviour. The presence of a snail whose eggs have a low viability rate could decrease their partners reproductive success