Modelling congenital transmission of Chagas` disease

The successful elimination of vectorial and transfusional transmission of Chagas` disease from some countries is a result of the reduction of domestic density of the primary vector Triatoma infestans, of almost 100% of coverage in blood serological selection and to the fact that the basic reproductive number of Chagas` disease is very close to one (1.25). Therefore, congenital transmission is currently the only way of acquiring Chagas` Disease in such regions. In this paper we propose a model of congenital transmission of Chagas` disease. Its aim is to provide an estimation of the time period it will take to eliminate this form of transmission in regions where vetorial transmission was reduced to close to zero, like in Brazil. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

FOR DEBATE A hypothesis for the 2007 dengue outbreak in Singapore

A previous mathematical model explaining dengue in Singapore predicted a reasonable outbreak of about 6500 cases for 2006 and a very mild outbreak with about 2000 cases for 2007. However, only 3051 cases were reported in 2006 while more than 7800 were reported in the first 44 weeks of 2007. We hypothesized that the combination of haze with other local sources of particulate matter had a significant impact on mosquito life expectancy, significantly increasing their mortality rate. To test the hypothesis a mathematical model based on the reproduction number of dengue fever and aimed at comparing the impact of several possible alternative control strategies was proposed. This model also aimed at contributing to the understanding of the causes of dengue resurgence in Singapore in the last decade. The model`s simulation demonstrated that an increase in mosquito mortality in 2006 and either a reduction in mortality or an increase in the carrying capacity of mosquitoes in 2007 explained the patterned observed in Singapore. Based on the model`s simulation we concluded that the fewer than expected number of dengue cases in Singapore in 2006 was caused by an increase in mosquito mortality due to the disproportionate haze affecting the country that year and that particularly favourable environmental conditions in 2007 propitiated mosquitoes with a lower mortality rate, which explains the greater than expected number of dengue cases in 2007. Whether our hypothesis is plausible or not should be debated further.

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.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Resurgence of HIV infection among men who have sex with men in Switzerland: mathematical modelling study.

BACKGROUND: New HIV infections in men who have sex with men (MSM) have increased in Switzerland since 2000 despite combination antiretroviral therapy (cART). The objectives of this mathematical modelling study were: to describe the dynamics of the HIV epidemic in MSM in Switzerland using national data; to explore the effects of hypothetical prevention scenarios; and to conduct a multivariate sensitivity analysis. METHODOLOGY/PRINCIPAL FINDINGS: The model describes HIV transmission, progression and the effects of cART using differential equations. The model was fitted to Swiss HIV and AIDS surveillance data and twelve unknown parameters were estimated. Predicted numbers of diagnosed HIV infections and AIDS cases fitted the observed data well. By the end of 2010, an estimated 13.5% (95% CI 12.5, 14.6%) of all HIV-infected MSM were undiagnosed and accounted for 81.8% (95% CI 81.1, 82.4%) of new HIV infections. The transmission rate was at its lowest from 1995-1999, with a nadir of 46 incident HIV infections in 1999, but increased from 2000. The estimated number of new infections continued to increase to more than 250 in 2010, although the reproduction number was still below the epidemic threshold. Prevention scenarios included temporary reductions in risk behaviour, annual test and treat, and reduction in risk behaviour to levels observed earlier in the epidemic. These led to predicted reductions in new infections from 2 to 26% by 2020. Parameters related to disease progression and relative infectiousness at different HIV stages had the greatest influence on estimates of the net transmission rate. CONCLUSIONS/SIGNIFICANCE: The model outputs suggest that the increase in HIV transmission amongst MSM in Switzerland is the result of continuing risky sexual behaviour, particularly by those unaware of their infection status. Long term reductions in the incidence of HIV infection in MSM in Switzerland will require increased and sustained uptake of effective interventions.

Chromosome studies in some Stevia. Cav. (Compositae) species from Southern Brazil

Karyotypes of six species of the genus Stevia from Southern Brazil were studied, utilizing root tip metaphases. All species were diploid with 2n = 22 chromosomes. It was possible to identify each species by chromosome morphology. The basic chromosome number for Brazilian species of Stevia is X = 11. This number is also found in almost all South American species. We suggest that in Stevia there is an evolutionary trend toward chromosomal rearrangement, caused mainly by pericentric inversions. It was found that, in addition to aneuploidy and polyploidy, chromosomal rearrangements are common in the tribe Eupatorieae.

Mitochondrial and chloroplast DNA-based phylogeny of Pelargonium (Geraniaceae)

Overall phylogenetic relationships within the genus Pelargonium (Geraniaceae) were inferred based on DNA sequences from mitochondrial(mt)-encoded nad1 b/c exons and from chloroplast(cp)-encoded trnL (UAA) 5' exon-trnF (GAA) exon regions using two species of Geranium and Sarcocaulon vanderetiae as outgroups. The group II intron between nad1 exons b and c was found to be absent from the Pelargonium, Geranium, and Sarcocaulon sequences presented here as well as from Erodium, which is the first recorded loss of this intron in angiosperms. Separate phylogenetic analyses of the mtDNA and cpDNA data sets produced largely congruent topologies, indicating linkage between mitochondrial and chloroplast genome inheritance. Simultaneous analysis of the combined data sets yielded a well-resolved topology with high clade support exhibiting a basic split into small and large chromosome species, the first group containing two lineages and the latter three. One large chromosome lineage (x = 11) comprises species from sections Myrrhidium and Chorisma and is sister to a lineage comprising P. mutans (x = 11) and species from section Jenkinsonia (x = 9). Sister to these two lineages is a lineage comprising species from sections Ciconium (x = 9) and Subsucculentia (x = 10). Cladistic evaluation of this pattern suggests that x = 11 is the ancestral basic chromosome number for the genus.

Cytogenetic characterization of Metynnis maculatus (Teleostei; Characiformes): the description in Serrasalminae of a small B chromosome bearing inactive NOR-like sequences

Mitotic chromosomes of Metynnis maculatus (KNER 1860) (Teleostei, Characiformes), a fish species that occurs in the Amazon and Parana-Paraguay river basins, were analyzed for the first time by Giemsa and Ag-NOR staining, C-banding and fluorescence in situ hybridization (FISH) with 18S and 5S rDNA sequences. The basic chromosome number of the species is 2n=62 (32M+22SM+4ST+4A) and, in addition to the 62 regular chromosomes, one small acrocentric supernumerary B chromosome was found in part of the specimens analyzed. Four active NORs were present, and constitutive heterochromatin blocks were found in the pericentromeric region of several chromosomes. A heterochromatic block was also present in the interstitial portion of the submetacentric NOR-bearing pair and the B chromosome was entirely heterochromatic. FISH using an 18S rDNA probe confirmed the results obtained with AgNO(3) staining, and an additional signal was also present on the B chromosomes. 5S rDNA sequences mapped only to the largest acrocentric pair. This is the first description of supernumerary B chromosomes in Serrasalminae, and this karyotype characterization may be useful in further studies about chromosome evolution in this fish group.

Traveling waves in the Lethargic Crab Disease

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

Modelling the lethargic crab disease.

The lethargic crab disease (LCD) is an emergent infirmity that has decimated native populations of the mangrove land crab (Ucides cordatus, Decapoda: Ocypodidae) along the Brazilian coast. Several potential etiological agents have been linked with LCD, but only in 2005 was it proved that it is caused by an ascomycete fungus. This is the first attempt to develop a mathematical model to describe the epidemiological dynamics of LCD. The model presents four possible scenarios, namely, the trivial equilibrium, the disease-free equilibrium, endemic equilibrium, and limit cycles arising from a Hopf bifurcation. The threshold values depend on the basic reproductive number of crabs and fungi, and on the infection rate. These scenarios depend on both the biological assumptions and the temporal evolution of the disease. Numerical simulations corroborate the analytical results and illustrate the different temporal dynamics of the crab and fungus populations.

Unusual occurrence of a ZZ/ZW sex-chromosome system and supernumerary chromosomes in Characidium cf. fasciatum (Pisces, Characiformes, Characidiinae)

Individuals of two populations of the fish Characidium cf. fasciatum were cytogenetically studied and showed a basic diploid number of 50 chromosomes. Some fishes were found to have 51 to 54 chromosomes due to the presence of one to four small subtelocentric/acrocentric supernumerary chromosomes. When analyzed by conventional Giemsa staining, male and female specimens of C. cf. fasciatum from the Quinta stream and Pardo River presented the same basic karyotypic macro- and microstructure, consisting of 32 metacentric and 18 submetacentric chromosomes.Ag-NORs were terminally located on the long arms of two submetacentric chromosome pairs. Constitutive heterochromatin was identified by C-banding as small pericentromeric blocks in the majority of the chromosomes, and B-chromosomes were found to be heterochromatic. The occurrence of one totally heterochromatic submetacentric chromosome restricted to females and considered as an unusual feature in fish karyotypes led to the identification of a ZZ/ZW sex-chromosome system. The implications of chromosomic differentiation observed in the genus Characidium are discussed.

Chromosome studies in some Stevia. Cav. (Compositae) species from Southern Brazil

Karyotypes of six species of the genus Stevia from Southern Brazil were studied, utilizing root tip metaphases. All species were diploid with 2n = 22 chromosomes. It was possible to identify each species by chromosome morphology. The basic chromosome number for Brazilian species of Stevia is X = 11. This number is also found in almost all South American species. We suggest that in Stevia there is an evolutionary trend toward chromosomal rearrangement, caused mainly by pericentric inversions. It was found that, in addition to aneuploidy and polyploidy, chromosomal rearrangements are common in the tribe Eupatorieae.

Karyotype analysis in Brachiaria (Poaceae) species

This is the first karyotype characterization of Brachiaria species. Twelve accessions belonging to five species were analysed. The basic chromosome number was x = 9 and 7, the same reported for the tribe Paniceae. Variations in the chromosome number were observed in B. decumbens (2n = 18; 36) and B. humidicola (20 = 36; 42; 54). Chromosome numbers of 20 = 18 in B. ruziziensis and 20 = 36 in B. brizantha and B. jubata were recorded. Inter- and intraspecific karyotype differentiation of the accessions analysed was facilitated by variations in karyotypic symmetry. The karyotypes were generally considered symmetrical, with a tendency to asymmetry in the direction of the polyploids. It is suggested that addition, deletions and mainly polyploidy have been the most direct causes involved in the chromosome evolution of this genus.