The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Case and partnership reproduction numbers for a curable sexually transmitted infection

Sexually transmitted infections (STIs) are, by definition, transmitted between sexual partners. For curable STIs an infected index case can potentially re-infect the same partner multiple times. Thus, R0, the average number of secondary infections one typical infected individual will produce during his or her infectious period is not necessarily the same as the average number of secondary cases (infected persons). Here we introduce the new concept of the case reproduction number (Rc). In addition, we define the partnership reproduction number (Rp) as the average number of secondary partnerships consisting of two infected individuals one typical infected individual will produce over his or her infectious lifetime. Rp takes into account clearance and re-infection within partnerships, which results in a prolongation of the duration of the infectious period. The two new reproduction numbers were derived for a deterministic pair model with serial monogamous partnerships using infection parameters for Chlamydia trachomatis, an example of a curable STI. We showed that re-infection within partnerships means that curable STIs can be sustained endemically even when the average number of secondary cases a person produces during his or her infectious period is below one.

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.

Perfil de Prudente de Moraes, Neto

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

DNA alignment and Bayesian trees of partial sequences of COI, COIII and the haemocyanin functional unit f-g of 28 octopod species

Background: Octopods have successfully colonised the world's oceans from the tropics to the poles. Yet, successful persistence in these habitats has required adaptations of their advanced physiological apparatus to compensate impaired oxygen supply. Their oxygen transporter haemocyanin plays a major role in cold tolerance and accordingly has undergone functional modifications to sustain oxygen release at sub-zero temperatures. However, it remains unknown how molecular properties evolved to explain the observed functional adaptations. We thus aimed to assess whether natural selection affected molecular and structural properties of haemocyanin that explains temperature adaptation in octopods. Results: Analysis of 239 partial sequences of the haemocyanin functional units (FU) f and g of 28 octopod species of polar, temperate, subtropical and tropical origin revealed natural selection was acting primarily on charge properties of surface residues. Polar octopods contained haemocyanins with higher net surface charge due to decreased glutamic acid content and higher numbers of basic amino acids. Within the analysed partial sequences, positive selection was present at site 2545, positioned between the active copper binding centre and the FU g surface. At this site, methionine was the dominant amino acid in polar octopods and leucine was dominant in tropical octopods. Sites directly involved in oxygen binding or quaternary interactions were highly conserved within the analysed sequence. Conclusions: This study has provided the first insight into molecular and structural mechanisms that have enabled octopods to sustain oxygen supply from polar to tropical conditions. Our findings imply modulation of oxygen binding via charge-charge interaction at the protein surface, which stabilize quaternary interactions among functional units to reduce detrimental effects of high pH on venous oxygen release. Of the observed partial haemocyanin sequence, residue 2545 formed a close link between the FU g surface and the active centre, suggesting a role as allosteric binding site. The prevalence of methionine at this site in polar octopods, implies regulation of oxygen affinity via increased sensitivity to allosteric metal binding. High sequence conservation of sites directly involved in oxygen binding indicates that functional modifications of octopod haemocyanin rather occur via more subtle mechanisms, as observed in this study.

Effects of pH on asexual reproduction and statolith formation of the scyphozoan, Aurelia labiata, 2010

Although anthropogenic infuences such as global warming, overfishing, and eutrophication may contribute to jellyfish blooms, little is known about the effects of ocean acidification on jellyfish. Most medusae form statoliths of calcium sulfate hemihydrate that are components of their balance organs (statocysts). This study was designed to test the effects of pH (7.9, within the average current range, 7.5, expected by 2100, and 7.2, expected by 2300) combined with two temperatures (9 and 15°C) on asexual reproduction and statolith formation of the moon jellyfish, Aurelia labiata. Polyp survival was 100% after 122 d in seawater in all six temperature and pH combinations. Because few polyps at 9°C strobilated, and temperature effects on budding were consistent with published results, we did not analyze data from those three treatments further. At 15°C, there were no significant effects of pH on the numbers of ephyrae or buds produced per polyp or on the numbers of statoliths per statocyst; however, statolith size was signi?cantly smaller in ephyrae released from polyps reared at low pH. Our results indicate that A. labiata polyps are quite tolerant of low pH, surviving and reproducing asexually even at the lowest tested pH; however, the effects of small statoliths on ephyra fitness are unknown. Future research on the behavior of ephyrae with small statoliths would further our understanding of how ocean acidi?cation may affect jellyfish survival in nature.

Reproduction in the squirrel glider, Petaurus norfolcensis (Petauridae) in south-east Queensland

Reproduction was studied across a three-year period in two south-east Queensland populations of the squirrel glider, Petaurus norfolcensis, by measuring morphological (body weight, scrotal diameter, cutaneous scent-gland activity, condition index) and physiological (plasma steroid levels) variables. Reproduction showed a seasonal pattern, with peak numbers of pouch young recorded in late autumn and winter. Declines in oestrogen concentrations outside the breeding period indicate that females are anoestrous in the summer months. Most (83%) reproductive females captured during the study were 2-3 years old, but all individuals over one year of age were found to have bred. Average litter size was 1.73 +/- 0.01 (n = 23). Scrotal diameter and testosterone concentrations showed no significant seasonal variation. It is suggested that this is due to the presence of both socially dominant and subordinate males in the data set. Maximum testosterone concentrations did coincide with periods of mating. The condition index showed no relationship with reproductive variables, but it is likely that this results from the manner in which the index was generated.

The Tetrahymena chaperonin subunit CCT eta gene is coexpressed with CCT gamma gene during cilia biogenesis and cell sexual reproduction

We report here the cloning and the characterization of the T. pyriformis CCT eta gene (TpCCT eta) and also a partial sequence of the corresponding T. thermophila gene (TtCCT eta). The TpCCt eta gene encodes a protein sharing a 60.3% identity with the mouse CCT eta. We have studied the expression of these genes in Tetrahymena exponentially growing cells, cells regenerating their cilia for different periods and during different stages of the cell sexual reproduction. These genes have similar patterns of expression to those of the previously identified TpCCt gamma gene. Indeed, the Tetrahymena CCT eta and CCT gamma genes are up-regulated at 60-120 min of cilia recovery, and in conjugation when vegetative growth was resumed and cell division took place. Our results seem to indicate that both CCT subunits play an important role in the biogenesis of the newly synthesized cilia of Tetrahymena and during its cell division.

Synchronous reproduction may facilitate introgression in a hybrid mussel (Mytilus) population

Mussel populations on the Irish Atlantic coast comprise an interbreeding mixture of the blue mussel, Mytilus edulis (L.) and the Mediterranean mussel, Mytilus galloprovincialis (Lmk.). The occurrence of hybrid genotypes varies between sites but can be as high 80%. This study compares the reproductive cycle of M. edulis, M. galloprovincialis and their hybrids to determine if the extensive hybridisation observed at Irish Atlantic coast sites is linked to spawning synchrony between the two taxa. Mussels (40-45 mm size class) were collected monthly from a sheltered shore in Galway Bay from January to December 2005. Two major spawning events (March- June and September-October) were observed and gametogenesis took place throughout the year. The spawning cycles of the three taxa were largely overlapping. Small differences were observed in the timing of peak spawning which occurred in March and October in M. galloprovincialis and in May-June and September in M.edulis. Spawning of hybrid individuals was intermediate between the parental genotypes. Fecundity was slightly higher in M. galloprovincialis females compared to the other taxa (up to 30% difference, p<0.05). This apparent advantage is not shared by the sexes and is likely being offset by high numbers of hybrid genotypes releasing gametes during peak spawning of M. galloprovincialis. There was no evidence for increased mortality in hybrid males; sex ratios did not deviate from the 1:1 ratio. The results show that in this region of the hybrid zone the timing of reproduction does not present a barrier to gene flow between M. edulis and M. galloprovincialis. Nonetheless, small differences in the timing of peak spawning may increase the likelihood of conspecific fertilisation at certain times of the year. Hybrids outnumber the parental genotypes, undergo complete gametogenesis and show no evidence of depressed fitness (i.e. hybrids are reproductively competent suggesting a high degree of introgression.

Reproduction and feeding ecology of Amphisbaena munoai and Anops kingi (Amphisbaenia, Amphisbaenidae) in the Escudo Sul-Rio-Grandense, southern Brazil

This study presents original data on the reproduction and feeding ecology of two syntopic amphisbaenians, Amphisbaena munoai Klappenbach, 1969 and Anops kingi Bell, 1833, from southern Brazil. Sampling was carried out from April 2004 to April 2006 at a highland area located in São Jerônimo and Barão do Triunfo municipalities, Rio Grande do Sul, Brazil. A total of 647 amphisbaenians were collected, 510 specimens of A. munoai and 137 specimens of A. kingi, of which 130 and 93, respectively, had their gonads and gut content analyzed. Both species presented a unimodal pattern of seasonal distribution, sexually mature females with significantly larger snout vent length (SVL) than sexually mature males, and seasonal reproductive cycle. Adults of A. kingi had significantly larger (SVL) than those of Amphisbaena munoai. Both species had generalist diets, but termites (Isoptera) was a staple item in their diet. Greater predominance of insect larvae was observed in the diet of A. kingi, which may be due to its larger body in comparison to A. munoai. Insect larvae ingested by A. kingi were significantly larger than those ingested by A. munoai. Diets of adult males and females of both species were not significantly different. The ontogenetic diet comparison in both species revealed significant numerical differences, with adults consuming higher numbers of prey.

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.

Use of unmodified starches and partial removal of serum to improve Granada medium stability

The use of 1% unmodified rice starch and 1% horse serum instead of 2% soluble starch and 5% serum in Granada medium is described. These components result in a medium of increased stability, preventing spoilage after a few days of storage at room temperature

Effect of an ectoparasite on reproduction in great tits.

1. The effect of a haematophageous ectoparasite, the hen flea, on quality an number of offspring was experimentally investigated in the great tit. The experiment consisted of a controlled infestation of a random sample of nests with the parasitic flea and of a regular treatment of control nests with Microwaves in order to eliminate the naturally occurring fleas. 2. To assess the effects of fleas on variables related to offspring number, we considered the number of hatchlings and fledglings, the mortality between hatching and fledging, and the hatching and fledging success. For assessment of offspring quality, we measured body mass, tarsus and wing length, and calculated the nutritional condition of, nestlings as the ratio of body mass to tarsus length. A physiological variable, the haematocrit level, was also measured. 3. Hatching success and hatchling numbers did not differ between the two experimental groups. Offspring mortality between hatching and fledging was significantly higher in the infested broods (xBAR = 0.22 chicks dead per day) than in the parasite-free broods (xBAR = 0.07 dead per day). Fledging success was 83% in the parasite-free broods, but only 53% in the infested ones. The number of fledglings in infested broods (xBAR = 3.7 fledglings +/-2.1 SD) was significantly lower than in the parasite-free (xBAR = 4.9 +/- 1.1 SD) broods. 4. Body mass of chicks in the infested broods was significantly smaller than in the parasite-free broods both 14 days and 17 days after hatching. The chicks in the infested broods reached a significantly smaller tarsus length than the ones in the parasite-free broods. Close to fledging, the nutritional condition of chicks was significantly lower in infested broods. Haematocrit levels were significantly lower in the infested broods. 5. Brood size correlated differently with body mass and condition of chicks in infested and parasite-free nests. In parasite-free broods both body mass and condition of chicks at age 17 days, i.e. close to fledging, were significantly higher in small broods than in large ones. However, in the infested broods chicks were of the same body mass and condition in large as in small broods. Therefore, in parasite-free broods fitness can potentially be gained through offspring quality or number or both, whereas in infested broods it can be gained through offspring quantity only. In other words, a trade-off between quality and number of offspring is feasible only in the absence of the parasitic hen flea. 6. These results emphasize the need to study the effects of ectoparasites on ecological, behavioural and evolutionary traits of their bird hosts. A knowledge of these effects is essential for the understanding of population dynamics, behaviour and life-history traits of the hosts.

Partial protection and intrathecal invasion of CD8(+) T cells in acute canine distemper virus infection.

Initial non-inflammatory demyelination in canine distemper virus infection (CDV) develops against a background of severe immunosuppression and is therefore, thought to be virus-induced. However, recently we found a marked invasion of T cells throughout the central nervous system (CNS) in dogs with acute distemper despite drastic damage to the immune system. In the present study, this apparent paradox was further investigated by immunophenotyping of lymphocytes, following experimental CDV challenge in vaccinated and non-vaccinated dogs. In contrast to CDV infected, unprotected dogs, vaccinated dogs did not become immunosuppressed and exhibited a strong antiviral immune response following challenge with virulent CDV. In unprotected dogs rapid and drastic lymphopenia was initially due to depletion of T cells. In peripheral blood, CD4(+) T cells were more sensitive and depleted earlier and for a longer time than CD8(+) cells which recovered soon. In the cerebrospinal fluid (CSF) we could observe an increase in the T cell to B cell and CD8(+) to CD4(+) ratios. Thus, partial protection of the CD8(+) cell population could explain why part of the immune function in acute distemper is preserved. As found earlier, T cells invaded the CNS parenchyma in these dogs but also in the protected challenged dogs, which did not develop any CNS disease at all. Since markers of T cell activation were upregulated in both groups of animals, this phenomenon could in part be related to non-specific penetration of activated T cells through the blood brain barrier. However, in diseased animals much larger numbers of T cells were found in the CNS than in the protected dogs, suggesting that massive invasion of T cells in the brain requires CDV expression in the CNS.

Effects of artisanal fisheries on the scorpaenids (Scorpaena spp.) reproduction in the marine protected area of Cap de Creus (NW Mediterranean)

Rockfish species are considered important to the ecology of rocky-reef communities which constitute a key habitat in many coastal marine protected areas (MPAs). These species, which are commercially valuable for artisanal fisheries in the Mediterranean, display particular biological traits that could render them vulnerable to fishing. In this study we monitored the artisanal fisheries of scorpaenids (Scorpaena spp.) in the MPA of Cap de Creus (northwestern Mediterranean) in order to estimate the status of their populations, to link captures with the reproduction of these species, and to evaluate the potential impact that artisanal fishing may have on them. Data from onboard sampling with artisanal fishermen and from fisheries statistics (total landings) were used. Total landings and catch per unit of effort (CPUE) follow a clearly seasonal cycle, with a prominent peak during the summer months coinciding with their spawning season, which may be due to mating behavior prior to fertilization. Although maximum sizes are bigger inside the MPA than in non-protected areas situated close by, a significant percentage of individuals caught inside the MPA are below their size at sexual maturity. Although rockfish seem to be favored by the partial protection of the MPA, the allowed artisanal fisheries are probably impacting the reproduction of these species