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Cutaneous Leishmaniasis (CL) is a vector-borne disease caused by a protozoan of the genus Leishmania and is considered one of the most important neglected tropical diseases. The Brazilian Amazon Forest harbors one of the highest diversity of Leishmania parasites and vectors and is one of the main focuses of the disease in the Americas. Previous studies showed that some types of anthropogenic disturbances have affected the abundance and distribution of CL vectors and hosts; however, few studies have thoroughly investigated the influence of different classes of land cover and land-use changes on the disease transmission risk. Here, we quantify the effect of land use and land-cover changes on the incidence of CL in all municipalities within the Brazilian Amazon Forest, from 2001 to 2017. We used a structured spatiotemporal Bayesian model to assess the effect of forest cover, agriculture, livestock, extractivism, and- deforestation on CL incidence, accounting for confounding variables such as population, climate, socioeconomic, and spatiotemporal random effects. We found that the increased risk of CL was associated with deforestation, especially modulated by a positive interaction between forest cover and livestock. Landscapes with ongoing deforestation for extensive cattle ranching are typically found in municipalities within the Amazon Frontier, where a high relative risk for CL was also identified. These findings provide valuable insights into developing effective public health policies and land-use planning to ensure healthier landscapes for people., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024. Published by Elsevier B.V.)

Brazil was one of the countries most affected during the first year of the COVID-19 pandemic, in a pre-vaccine era, and mathematical and statistical models were used in decision-making and public policies to mitigate and suppress SARS-CoV-2 dispersion. In this article, we intend to overview the modeling for COVID-19 in Brazil, focusing on the first 18 months of the pandemic. We conducted a scoping review and searched for studies on infectious disease modeling methods in peer-reviewed journals and gray literature, published between January 01, 2020, and June 2, 2021, reporting real-world or scenario-based COVID-19 modeling for Brazil. We included 81 studies, most corresponding to published articles produced in Brazilian institutions. The models were dynamic and deterministic in the majority. The predominant model type was compartmental, but other models were also found. The main modeling objectives were to analyze epidemiological scenarios (testing interventions' effectiveness) and to project short and long-term predictions, while few articles performed economic impact analysis. Estimations of the R0 and transmission rates or projections regarding the course of the epidemic figured as major, especially at the beginning of the crisis. However, several other outputs were forecasted, such as the isolation/quarantine effect on transmission, hospital facilities required, secondary cases caused by infected children, and the economic effects of the pandemic. This study reveals numerous articles with shared objectives and similar methods and data sources. We observed a deficiency in addressing social inequities in the Brazilian context within the utilized models, which may also be expected in several low- and middle-income countries with significant social disparities. We conclude that the models were of great relevance in the pandemic scenario of COVID-19. Nevertheless, efforts could be better planned and executed with improved institutional organization, dialogue among research groups, increased interaction between modelers and epidemiologists, and establishment of a sustainable cooperation network., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Berg de Almeida et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Background: Vaccines developed between 2020 and 2021 against the SARS-CoV-2 virus were designed to diminish the severity and prevent deaths due to COVID-19. However, estimates of the effectiveness of vaccination campaigns in achieving these goals remain a methodological challenge. In this work, we developed a Bayesian statistical model to estimate the number of deaths and hospitalisations averted by vaccination of older adults (above 60 years old) in Brazil., Methods: We fit a linear model to predict the number of deaths and hospitalisations of older adults as a function of vaccination coverage in this group and casualties in younger adults. We used this model in a counterfactual analysis, simulating alternative scenarios without vaccination or with faster vaccination roll-out. We estimated the direct effects of COVID-19 vaccination by computing the difference between hypothetical and realised scenarios., Findings: We estimated that more than 165,000 individuals above 60 years of age were not hospitalised due to COVID-19 in the first seven months of the vaccination campaign. An additional contingent of 104,000 hospitalisations could have been averted if vaccination had started earlier. We also estimated that more than 58 thousand lives were saved by vaccinations in the period analysed for the same age group and that an additional 47 thousand lives could have been saved had the Brazilian government started the vaccination programme earlier., Interpretation: Our estimates provided a lower bound for vaccination impacts in Brazil, demonstrating the importance of preventing the suffering and loss of older Brazilian adults. Once vaccines were approved, an early vaccination roll-out could have saved many more lives, especially when facing a pandemic., Funding: The Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brazil (Finance Code 001 to F.M.D.M. and L.S.F.), Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brazil (grant number: 315854/2020-0 to M.E.B., 141698/2018-7 to R.L.P.d.S., 313055/2020-3 to P.I.P., 311832/2017-2 to R.A.K.), Fundação de Amparo à Pesquisa do Estado de São Paulo - Brazil (contract number: 2016/01343-7 to R.A.K.), Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro - Brazil (grant number: E-26/201.277/2021 to L.S.B.) and Inova Fiocruz/Fundação Oswaldo Cruz - Brazil (grant number: 48401485034116) to L.S.B., O.G.C. and M.G.d.F.C. The funding agencies had no role in the conceptualization of the study., Competing Interests: The authors acknowledge the funding agencies: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil (Finance Code 001 to FMDM and LSF), Conselho Nacional de Desenvolvimento Científico e Tecnológico – Brazil (grant number: 315854/2020-0 to MEB, 141698/2018-7 to RLPS, 313055/2020-3 to PIP, 311832/2017-2 to RAK), Fundação de Amparo à Pesquisa do Estado de São Paulo – Brazil (contract number: 2016/01343-7 to RAK), Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro – Brazil (grant number: E-26/201.277/2021 to LSB) and Inova Fiocruz/Fundação Oswaldo Cruz – Brazil (grant number: VPPCB-005-FIO-20-2-50) to LSB, OGC and MGFC. The funding agencies had no role in the conceptualization of the study., (© 2022 The Author(s).)

Background: Developing countries have experienced significant COVID-19 disease burden. With the emergence of new variants, particularly omicron, the disease burden in children has increased. When the first COVID-19 vaccine was approved for use in children aged 5-11 years of age, very few countries recommended vaccination due to limited risk-benefit evidence for vaccination of this population. In Brazil, ranking second in the global COVID-19 death toll, the childhood COVID-19 disease burden increased significantly in early 2022. This prompted a risk-benefit assessment of the introduction and scaling-up of COVID-19 vaccination of children., Methods: To estimate the potential impact of vaccinating children aged 5-11 years with mRNA-based COVID-19 vaccine in the context of omicron dominance, we developed a discrete-time SEIR-like model stratified in age groups, considering a three-month time horizon. We considered three scenarios: No vaccination, slow, and maximum vaccination paces. In each scenario, we estimated the potential reduction in total COVID-19 cases, hospitalizations, deaths, hospitalization costs, and potential years of life lost, considering the absence of vaccination as the base-case scenario., Findings: We estimated that vaccinating at a maximum pace could prevent, between mid-January and April 2022, about 26,000 COVID-19 hospitalizations, and 4200 deaths in all age groups; of which 5400 hospitalizations and 410 deaths in children aged 5-11 years. Continuing vaccination at a slow/current pace would prevent 1450 deaths and 9700 COVID-19 hospitalizations in all age groups in this same time period; of which 180 deaths and 2390 hospitalizations in children only., Interpretation: Maximum vaccination of children results in a significant reduction of COVID-19 hospitalizations and deaths and should be enforced in developing countries with significant disease incidence in children., Funding: This manuscript was funded by the Brazilian Council for Scientific and Technology Development (CNPq - Process # 402834/2020-8)., Competing Interests: MEB received payment fees for consulting service for work on database management in the municipality of Florianópolis, funded by 10.13039/100011893PAHO/10.13039/100004423WHO (contract number CON21-00014067). All authors declare no conflict of interest., (© 2022 The Author(s).)

We simulate the impact of school reopening during the COVID-19 pandemic in three major urban centers in Brazil to identify the epidemiological indicators and the best timing for the return of in-school activities and the effect of contact tracing as a mitigation measure. Our goal is to offer guidelines for evidence-based policymaking. We implement an extended SEIR model stratified by age and considering contact networks in different settings - school, home, work, and community, in which the infection transmission rate is affected by various intervention measures. After fitting epidemiological and demographic data, we simulate scenarios with increasing school transmission due to school reopening, and also estimate the number of hospitalization and deaths averted by the implementation of contact tracing. Reopening schools results in a non-linear increase in reported COVID-19 cases and deaths, which is highly dependent on infection and disease incidence at the time of reopening. When contact tracing and quarantining are restricted to school and home settings, a large number of daily tests is required to produce significant effects in reducing the total number of hospitalizations and deaths. Policymakers should carefully consider the epidemiological context and timing regarding the implementation of school closure and return of in-person school activities. While contact tracing strategies prevent new infections within school environments, they alone are not sufficient to avoid significant impacts on community transmission., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 Published by Elsevier Inc.)

Introduction: Brazil experienced moments of collapse in its health system throughout 2021, driven by the emergence of variants of concern (VOC) combined with an inefficient initial vaccination strategy against Covid-19., Objectives: To support decision-makers in formulating COVID-19 immunization policy in the context of limited vaccine availability and evolving variants over time, we evaluate optimal strategies for Covid-19 vaccination in Brazil in 2021, when vaccination was rolled out during Gamma variant predominance., Methods: Using a discrete-time epidemic model we estimate Covid-19 deaths averted, considering the currently Covid-19 vaccine products and doses available in Brazil; vaccine coverage by target population; and vaccine effectiveness estimates. We evaluated a 5-month time horizon, from early August to the end of December 2021. Optimal vaccination strategies compared the outcomes in terms of averted deaths when varying dose intervals from 8 to 12 weeks, and choosing the minimum coverage levels per age group required prior to expanding vaccination to younger target populations. We also estimated dose availability required over time to allow the implementation of optimal strategies., Results: To maximize the number of averted deaths, vaccine coverage of at least 80 % should be reached in older age groups before starting vaccination into subsequent younger age groups. When evaluating varying dose intervals for AZD1222, reducing the dose interval from 12 to 8 weeks for the primary schedule would result in fewer COVID-19 deaths, but this can only be implemented if accompanied by an increase in vaccine supply of at least 50 % over the coming six-months in Brazil., Conclusion: Covid-19 immunization strategies should be tailored to local vaccine product availability and supply over time, circulating variants of concern, and vaccine coverage in target population groups. Modelling can provide valuable and timely evidence to support the implementation of vaccination strategies considering the local context, yet following international and regional technical evidence-based guidance., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Since the emergence of the novel coronavirus disease 2019 (COVID-19), mathematical modelling has become an important tool for planning strategies to combat the pandemic by supporting decision-making and public policies, as well as allowing an assessment of the effect of different intervention scenarios. A proliferation of compartmental models were developed by the mathematical modelling community in order to understand and make predictions about the spread of COVID-19. While compartmental models are suitable for simulating large populations, the underlying assumption of a well-mixed population might be problematic when considering non-pharmaceutical interventions (NPIs) which have a major impact on the connectivity between individuals in a population. Here we propose a modification to an extended age-structured SEIR (susceptible-exposed-infected-recovered) framework, with dynamic transmission modelled using contact matrices for various settings in Brazil. By assuming that the mitigation strategies for COVID-19 affect the connections among different households, network percolation theory predicts that the connectivity among all households decreases drastically above a certain threshold of removed connections. We incorporated this emergent effect at population level by modulating home contact matrices through a percolation correction function, with the few additional parameters fitted to hospitalisation and mortality data from the city of São Paulo. Our model with percolation effects was better supported by the data than the same model without such effects. By allowing a more reliable assessment of the impact of NPIs, our improved model provides a better description of the epidemiological dynamics and, consequently, better policy recommendations., (Copyright © 2022 The Authors. Published by Elsevier B.V. All rights reserved.)

The SARS-CoV-2 pandemic is a major concern all over the world and, as vaccines became available at the end of 2020, optimal vaccination strategies were subjected to intense investigation. Considering their critical role in reducing disease burden, the increasing demand outpacing production, and that most currently approved vaccines follow a two-dose regimen, the cost-effectiveness of delaying the second dose to increment the coverage of the population receiving the first dose is often debated. Finding the best solution is complex due to the trade-off between vaccinating more people with lower level of protection and guaranteeing higher protection to a fewer number of individuals. Here we present a novel extended age-structured SEIR mathematical model that includes a two-dose vaccination schedule with a between-doses delay modelled through delay differential equations and linear optimization of vaccination rates. By maintaining the minimum stock of vaccines under a given production rate, we evaluate the dose interval that minimizes the number of deaths. We found that the best strategy depends on an interplay between the vaccine production rate and the relative efficacy of the first dose. In the scenario of low first-dose efficacy, it is always better to vaccinate the second dose as soon as possible, while for high first-dose efficacy, the best strategy of time window depends on the production rate and also on second-dose efficacy provided by each type of vaccine. We also found that the rate of spread of the infection does not affect significantly the thresholds of the best window, but is an important factor in the absolute number of total deaths. These conclusions point to the need to carefully take into account both vaccine characteristics and roll-out speed to optimize the outcome of vaccination strategies., Competing Interests: The authors have declared that no competing interests exist.

Background: The SARS-CoV-2 variant of concern (VOC) P.1 (Gamma variant) emerged in the Amazonas State, Brazil, in November 2020. The epidemiological consequences of its mutations have not been widely studied, despite detection of P.1 in 36 countries, with local transmission in at least 5 countries. A range of mutations are seen in P.1, ten of them in the spike protein. It shares mutations with VOCs previously detected in the United Kingdom (B.1.1.7, Alpha variant) and South Africa (B.1.351, Beta variant)., Methods: We estimated the transmissibility and reinfection of P.1 using a model-based approach, fitting data from the national health surveillance of hospitalized individuals and frequency of the P.1 variant in Manaus from December-2020 to February-2021., Results: Here we estimate that the new variant is about 2.6 times more transmissible (95% Confidence Interval: 2.4-2.8) than previous circulating variant(s). Manaus already had a high prevalence of individuals previously affected by the SARS-CoV-2 virus and our fitted model attributed 28% of Manaus cases in the period to reinfections by P.1, confirming the importance of reinfection by this variant. This value is in line with estimates from blood donors samples in Manaus city., Conclusions: Our estimates rank P.1 as one of the most transmissible among the SARS-CoV-2 VOCs currently identified, and potentially as transmissible as the posteriorly detected VOC B.1.617.2 (Delta variant), posing a serious threat and requiring measures to control its global spread., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2021.)

Background: Cutaneous leishmaniasis (CL) is a vector-borne disease classified by the World Health Organization as one of the most neglected tropical diseases. Brazil has the highest incidence of CL in America and is one of the ten countries in the world with the highest number of cases. Understanding the spatiotemporal dynamics of CL is essential to provide guidelines for public health policies in Brazil. In the present study we used a spatial and temporal statistical approach to evaluate the dynamics of CL in Brazil., Methods: We used data of cutaneous leishmaniasis cases provided by the Ministry of Health of Brazil from 2001 to 2017. We calculated incidence rates and used the Mann-Kendall trend test to evaluate the temporal trend of CL in each municipality. In addition, we used Kuldorff scan method to identify spatiotemporal clusters and emerging hotspots test to evaluate hotspot areas and their temporal trends., Results: We found a general decrease in the number of CL cases in Brazil (from 15.3 to 8.4 cases per 100 000 habitants), although 3.2% of municipalities still have an increasing tendency of CL incidence and 72.5% showed no tendency at all. The scan analysis identified a primary cluster in northern and central regions and 21 secondary clusters located mainly in south and southeast regions. The emerging hotspots analysis detected a high spatial and temporal variability of hotspots inside the main cluster area, diminishing hotspots in eastern Amazon and permanent, emerging, and new hotspots in the states of Amapá and parts of Pará, Roraima, Acre and Mato Grosso. The central coast the state of Bahia is one of the most critical areas due to the detection of a cluster of the highest rank in a secondary cluster, and because it is the only area identified as an intensifying hotspot., Conclusions: Using a combination of statistical methods we were able to detect areas of higher incidence of CL and understand how it changed over time. We suggest that these areas, especially those identified as permanent, new, emerging and intensifying hotspots, should be targeted for future research, surveillance, and implementation of vector control measures.

This article discusses the epidemic situation of Covid-19 in Brazil, in the face of the emergence of a new strain called P.1, which is more transmissible and may be associated with reinfection. Given the collapse of hospital care in Manaus in January 2021 and the results of three recent preprints, each that reports increased transmissibility of the P.1 variant, we propose some urgent measures. Genomic surveillance based on multi-step diagnostics, starting with RT-PCR type tests and up to sequencing, should be established. Efforts to identify reinfections associated with this variant and the update of its definition in protocols should be prioritized, and studies on the efficacy of currently available vaccines in Brazil concerning the new variant should be conducted. We also propose improving the Brazilian health surveillance system such that genomic surveillance is coordinated and thereby better able to respond to future emergencies in a more timely fashion. We call on the public agents involved in health surveillance to share data and information regarding the epidemic in a clear, fast and transparent way. Finally, we propose a greater engagement in inter-institutional cooperation of all those involved in the response and production of knowledge about the pandemic in our country.

In this work we analyze potential environmental drivers of malaria cases in Northwestern Argentina. We inspect causal links between malaria and climatic variables by means of the convergent cross mapping technique, which provides a causality criterion from the theory of dynamic systems. Analysis is based on 12 years of weekly malaria P. vivax cases in Tartagal, Salta, Argentina-at the southern fringe of malaria incidence in the Americas-together with humidity and temperature time-series spanning the same period. Our results show that there are causal links between malaria cases and both maximum temperature, with a delay of five weeks, and minimum temperature, with delays of zero and twenty two weeks. Humidity is also a driver of malaria cases, with thirteen weeks delay between cause and effect. Furthermore we also determined the sign and strength of the effects. Temperature has always a positive non-linear effect on cases, with maximum temperature effects more pronounced above 25°C and minimum above 17°C, while effects of humidity are more intricate: maximum humidity above 85% has a negative effect, whereas minimum humidity has a positive effect on cases. These results might be signaling processes operating at short (below 5 weeks) and long (over 12 weeks) time delays, corresponding to effects related to parasite cycle and mosquito population dynamics respectively. The non-linearities found for the strength of the effect of temperature on malaria cases make warmer areas more prone to higher increases in the disease incidence. Moreover, our results indicate that an increase of extreme weather events could enhance the risks of malaria spreading and re-emergence beyond the current distribution. Both situations, warmer climate and increase of extreme events, will be remarkably increased by the end of the century in this hot spot of climate change., Competing Interests: The authors have declared that no competing interests exist.

Groups in nature can be formed by interactions between individuals, or by external pressures like predation. It is reasonable to assume that groups formed by internal and external conditions have different dynamics and structures. We propose a computational model to investigate the effects of individual recognition on the formation and structure of animal groups. Our model is composed of agents that can recognize each other and remember previous interactions, without any external pressures, in order to isolate the effects of individual recognition. We show that individual recognition affects the number and size of groups, and the modularity of the social networks. This model can be used as a null model to investigate the effects of external factors on group formation and persistence., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: RAK is currently an Academic Editor for PLOS ONE. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

The relation between rainfall and water accumulated in reservoirs comprises nonlinear feedbacks. Here we show that they may generate alternative equilibrium regimes, one of high water-volume, the other of low water-volume. Reservoirs can be seen as socio-environmental systems at risk of regime shifts, characteristic of tipping point transitions. We analyze data from stored water, rainfall, and water inflow and outflow in the main reservoir serving the metropolitan area of São Paulo, Brazil, by means of indicators of critical regime shifts, and find a strong signal of a transition. We furthermore build a mathematical model that gives a mechanistic view of the dynamics and demonstrates that alternative stable states are an expected property of water reservoirs. We also build a stochastic version of this model that fits well to the data. These results highlight the broader aspect that reservoir management must account for their intrinsic bistability, and should benefit from dynamical systems theory. Our case study illustrates the catastrophic consequences of failing to do so.

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Habitat split is a major force behind the worldwide decline of amphibian populations, causing community change in richness and species composition. In fragmented landscapes, natural remnants, the terrestrial habitat of the adults, are frequently separated from streams, the aquatic habitat of the larvae. An important question is how this landscape configuration affects population levels and if it can drive species to extinction locally. Here, we put forward the first theoretical model on habitat split which is particularly concerned on how split distance - the distance between the two required habitats - affects population size and persistence in isolated fragments. Our diffusive model shows that habitat split alone is able to generate extinction thresholds. Fragments occurring between the aquatic habitat and a given critical split distance are expected to hold viable populations, while fragments located farther away are expected to be unoccupied. Species with higher reproductive success and higher diffusion rate of post-metamorphic youngs are expected to have farther critical split distances. Furthermore, the model indicates that negative effects of habitat split are poorly compensated by positive effects of fragment size. The habitat split model improves our understanding about spatially structured populations and has relevant implications for landscape design for conservation. It puts on a firm theoretical basis the relation between habitat split and the decline of amphibian populations.

Background: Plasmodium vivax is a widely distributed, neglected parasite that can cause malaria and death in tropical areas. It is associated with an estimated 80-300 million cases of malaria worldwide. Brazilian tropical rain forests encompass host- and vector-rich communities, in which two hypothetical mechanisms could play a role in the dynamics of malaria transmission. The first mechanism is the dilution effect caused by presence of wild warm-blooded animals, which can act as dead-end hosts to Plasmodium parasites. The second is diffuse mosquito vector competition, in which vector and non-vector mosquito species compete for blood feeding upon a defensive host. Considering that the World Health Organization Malaria Eradication Research Agenda calls for novel strategies to eliminate malaria transmission locally, we used mathematical modeling to assess those two mechanisms in a pristine tropical rain forest, where the primary vector is present but malaria is absent., Methodology/principal Findings: The Ross-Macdonald model and a biodiversity-oriented model were parameterized using newly collected data and data from the literature. The basic reproduction number ([Formula: see text]) estimated employing Ross-Macdonald model indicated that malaria cases occur in the study location. However, no malaria cases have been reported since 1980. In contrast, the biodiversity-oriented model corroborated the absence of malaria transmission. In addition, the diffuse competition mechanism was negatively correlated with the risk of malaria transmission, which suggests a protective effect provided by the forest ecosystem. There is a non-linear, unimodal correlation between the mechanism of dead-end transmission of parasites and the risk of malaria transmission, suggesting a protective effect only under certain circumstances (e.g., a high abundance of wild warm-blooded animals)., Conclusions/significance: To achieve biological conservation and to eliminate Plasmodium parasites in human populations, the World Health Organization Malaria Eradication Research Agenda should take biodiversity issues into consideration.

This paper presents a mathematical model for cholera epidemics which comprises seasonality, loss of host immunity, and control mechanisms acting to reduce cholera transmission. A collection of data related to cholera disease allows us to show that outbreaks in endemic areas are subject to a resonant behavior, since the intrinsic oscillation period of the disease (∼1 year) is synchronized with the annual contact rate variation. Moreover, we argue that the short period of the host immunity may be associated to secondary peaks of incidence observed in some regions (a bimodal pattern). Finally, we explore some possible mechanisms of cholera control, and analyze their efficiency. We conclude that, besides mass vaccination--which may be impracticable--improvements in sanitation system and food/personal hygiene are the most effective ways to prevent an epidemic.

We examine the classical problem of the existence of a threshold size for a patch to allow for survival of a given population in the case where the patch is not completely isolated. The surrounding habitat matrix is characterized by a non-zero carrying capacity. We show that a critical patch size cannot be strictly defined in this case. We also obtain the saturation density in such a patch as a function of the size of the patch and the relative carrying capacity of the outer region. We argue that this relative carrying capacity is a measure of the isolation of the patch. Our results are then compared with conclusions drawn from observations of the population dynamics of understorey birds in fragments of the Amazonian forest and shown to qualitatively agree with them, offering an explanation for the importance of dispersal and isolation in these observations. Finally, we show that a generalized critical patch size can be introduced resorting to threshold densities for the observation of a given species.

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case.

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of the damped Benjamin-Ono equation. The structure of the dispersive shock is considered in this method.

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the special case theta=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis.

Using a variational approach we have studied the shape preserving coherent propagation of light pulses in a resonant dispersive medium in the presence of the Kerr nonlinearity. Within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations, we show the existence of a solitary wave. We have tested our analytical solution through numerical simulations confirming its solitary wave nature.

Asymptotic behavior of initially "large and smooth" pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrödinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp upsilon(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good agreement is obtained between the analytical and numerical results.

In this paper we discuss the propagation of nonlinear electromagnetic short waves in ferromagnetic insulators. We show that such propagation is perpendicular to an externally applied field. In the nonlinear regime we determine various possible propagation patterns: an isolated pulse, a modulated sinusoidal wave, and an asymptotic two-peak wave. The mathematical structure underlying the existence of these solutions is that of the integrable sine-Gordon equation.

In this paper we study the interplay between short- and long-space scales in the context of conservative dispersive systems. We consider model systems in (1+1) dimensions that admit both long- and short-wavelength solutions in the linear regime. A nonlinear analysis of these systems is constructed, making use of multiscale expansions. We show that the equations governing the lowest order involve only short-wave properties and that the long-wave effects to leading order are determined by a secularity elimination procedure.