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de Araújo RGS, Jorge DCP, Dorn RC, Cruz-Pacheco G, Esteva MLM, Pinho STR. Applying a multi-strain dengue model to epidemics data. Math Biosci 2023; 360:109013. [PMID: 37127090 DOI: 10.1016/j.mbs.2023.109013] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Revised: 04/17/2023] [Accepted: 04/24/2023] [Indexed: 05/03/2023]
Abstract
Dengue disease transmission is a complex vector-borne disease, mainly due to the co-circulation of four serotypes of the virus. Mathematical models have proved to be a useful tool to understand the complexity of this disease. In this work, we extend the model studied by Esteva et al., 2003, originally proposed for two serotypes, to four circulating serotypes. Using epidemic data of dengue fever in Iquitos (Peru) and San Juan (Puerto Rico), we estimate numerically the co-circulation parameter values for selected outbreaks using a bootstrap method, and we also obtained the Basic Reproduction Number, R0, for each serotype, using both analytical calculations and numerical simulations. Our results indicate that the impact of co-circulation of serotypes in population dynamics of dengue infection is such that there is a reduced effect from DENV-3 to DENV-4 in comparison to no-cross effect for epidemics in Iquitos. Concerning San Juan epidemics, also comparing to no-cross effect, we also observed a reduced effect from the predominant serotype DENV-3 to both DENV-2 and DENV-1 epidemics neglecting the very small number of cases of DENV-4.
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Affiliation(s)
| | - Daniel C P Jorge
- Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil; Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil.
| | - Rejane C Dorn
- Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil.
| | - Gustavo Cruz-Pacheco
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Autónoma de México, Cuidad de México, Mexico.
| | - M Lourdes M Esteva
- Facultad de Ciências, Universidad Autónoma de México, Cuidad de México, Mexico.
| | - Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Brazil; Instituto Nacional de Ciência e Tecnologia - Sistemas Complexos, Brazil.
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2
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Pinho STR. Some features on methodology of dengue modelling linked to data: Comment on "Mathematical modelling for dengue fever epidemiology: a 10-year systematic review" by M. Aguiar et al. Phys Life Rev 2023; 44:276-278. [PMID: 36821892 PMCID: PMC9916129 DOI: 10.1016/j.plrev.2023.01.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2023] [Accepted: 01/30/2023] [Indexed: 02/12/2023]
Affiliation(s)
- Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia, 40170-115, Salvador, Brazil; Instituto Nacional de Ciência e Tecnologia - Sistemas Complexos, Brazil.
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3
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Jorge DCP, Oliveira JF, Miranda JGV, Andrade RFS, Pinho STR. Estimating the effective reproduction number for heterogeneous models using incidence data. R Soc Open Sci 2022; 9:220005. [PMID: 36133147 DOI: 10.6084/m9.figshare.c.6167795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 08/16/2022] [Indexed: 05/25/2023]
Abstract
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
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Affiliation(s)
- D C P Jorge
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - J F Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - J G V Miranda
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - R F S Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - S T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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4
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Jorge DCP, Oliveira JF, Miranda JGV, Andrade RFS, Pinho STR. Estimating the effective reproduction number for heterogeneous models using incidence data. R Soc Open Sci 2022; 9:220005. [PMID: 36133147 DOI: 10.5281/zenodo.5822669] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 08/16/2022] [Indexed: 05/25/2023]
Abstract
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
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Affiliation(s)
- D C P Jorge
- Instituto de Física Teórica, Universidade Estadual Paulista-UNESP, R. Dr. Teobaldo Ferraz 271, São Paulo 01140-070, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - J F Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - J G V Miranda
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - R F S Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - S T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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5
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Jorge DCP, Rodrigues MS, Silva MS, Cardim LL, da Silva NB, Silveira IH, Silva VAF, Pereira FAC, de Azevedo AR, Amad AAS, Pinho STR, Andrade RFS, Ramos PIP, Oliveira JF. Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil. Epidemics 2021; 35:100465. [PMID: 33984687 DOI: 10.1101/2020.06.26.20140780] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Revised: 03/13/2021] [Accepted: 04/30/2021] [Indexed: 05/25/2023] Open
Abstract
COVID-19 is now identified in almost all countries in the world, with poorer regions being particularly more disadvantaged to efficiently mitigate the impacts of the pandemic. In the absence of efficient therapeutics or large-scale vaccination, control strategies are currently based on non-pharmaceutical interventions, comprising changes in population behavior and governmental interventions, among which the prohibition of mass gatherings, closure of non-essential establishments, quarantine and movement restrictions. In this work we analyzed the effects of 707 governmental interventions published up to May 22, 2020, and population adherence thereof, on the dynamics of COVID-19 cases across all 27 Brazilian states, with emphasis on state capitals and remaining inland cities. A generalized SEIR (Susceptible, Exposed, Infected and Removed) model with a time-varying transmission rate (TR), that considers transmission by asymptomatic individuals, is presented. We analyze the effect of both the extent of enforced measures across Brazilian states and population movement on the changes in the TR and effective reproduction number. The social mobility reduction index, a measure of population movement, together with the stringency index, adapted to incorporate the degree of restrictions imposed by governmental regulations, were used in conjunction to quantify and compare the effects of varying degrees of policy strictness across Brazilian states. Our results show that population adherence to social distance recommendations plays an important role for the effectiveness of interventions and represents a major challenge to the control of COVID-19 in low- and middle-income countries.
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Affiliation(s)
- Daniel C P Jorge
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | | | - Mateus S Silva
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Luciana L Cardim
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Nívea B da Silva
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil; Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Ismael H Silveira
- Instituto de Saúde Coletiva, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Vivian A F Silva
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | | | - Arthur R de Azevedo
- Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Alan A S Amad
- College of Engineering, Swansea University, Swansea, Wales, United Kingdom
| | - Suani T R Pinho
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Roberto F S Andrade
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil; Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Pablo I P Ramos
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Juliane F Oliveira
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil; Centre of Mathematics of the University of Porto (CMUP), Department of Mathematics, Porto, Portugal.
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6
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Jorge DCP, Rodrigues MS, Silva MS, Cardim LL, da Silva NB, Silveira IH, Silva VAF, Pereira FAC, de Azevedo AR, Amad AAS, Pinho STR, Andrade RFS, Ramos PIP, Oliveira JF. Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil. Epidemics 2021; 35:100465. [PMID: 33984687 PMCID: PMC8106524 DOI: 10.1016/j.epidem.2021.100465] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Revised: 03/13/2021] [Accepted: 04/30/2021] [Indexed: 12/14/2022] Open
Abstract
COVID-19 is now identified in almost all countries in the world, with poorer regions being particularly more disadvantaged to efficiently mitigate the impacts of the pandemic. In the absence of efficient therapeutics or large-scale vaccination, control strategies are currently based on non-pharmaceutical interventions, comprising changes in population behavior and governmental interventions, among which the prohibition of mass gatherings, closure of non-essential establishments, quarantine and movement restrictions. In this work we analyzed the effects of 707 governmental interventions published up to May 22, 2020, and population adherence thereof, on the dynamics of COVID-19 cases across all 27 Brazilian states, with emphasis on state capitals and remaining inland cities. A generalized SEIR (Susceptible, Exposed, Infected and Removed) model with a time-varying transmission rate (TR), that considers transmission by asymptomatic individuals, is presented. We analyze the effect of both the extent of enforced measures across Brazilian states and population movement on the changes in the TR and effective reproduction number. The social mobility reduction index, a measure of population movement, together with the stringency index, adapted to incorporate the degree of restrictions imposed by governmental regulations, were used in conjunction to quantify and compare the effects of varying degrees of policy strictness across Brazilian states. Our results show that population adherence to social distance recommendations plays an important role for the effectiveness of interventions and represents a major challenge to the control of COVID-19 in low- and middle-income countries.
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Affiliation(s)
- Daniel C P Jorge
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | | | - Mateus S Silva
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Luciana L Cardim
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Nívea B da Silva
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil; Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Ismael H Silveira
- Instituto de Saúde Coletiva, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Vivian A F Silva
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | | | - Arthur R de Azevedo
- Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Alan A S Amad
- College of Engineering, Swansea University, Swansea, Wales, United Kingdom
| | - Suani T R Pinho
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Roberto F S Andrade
- Instituto de Fısica, Universidade Federal da Bahia, Salvador, Bahia, Brazil; Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Pablo I P Ramos
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil
| | - Juliane F Oliveira
- Center for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Bahia, Brazil; Centre of Mathematics of the University of Porto (CMUP), Department of Mathematics, Porto, Portugal.
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7
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Oliveira JF, Jorge DCP, Veiga RV, Rodrigues MS, Torquato MF, da Silva NB, Fiaccone RL, Cardim LL, Pereira FAC, de Castro CP, Paiva ASS, Amad AAS, Lima EABF, Souza DS, Pinho STR, Ramos PIP, Andrade RFS. Mathematical modeling of COVID-19 in 14.8 million individuals in Bahia, Brazil. Nat Commun 2021; 12:333. [PMID: 33436608 PMCID: PMC7803757 DOI: 10.1038/s41467-020-19798-3] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Accepted: 10/26/2020] [Indexed: 12/30/2022] Open
Abstract
COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase in R0. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses.
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Affiliation(s)
- Juliane F Oliveira
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil.
- Centre of Mathematics of the University of Porto (CMUP), Department of Mathematics, Porto, Portugal.
| | - Daniel C P Jorge
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Rafael V Veiga
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | | | | | - Nivea B da Silva
- Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Rosemeire L Fiaccone
- Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Luciana L Cardim
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | | | - Caio P de Castro
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Aureliano S S Paiva
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - Alan A S Amad
- College of Engineering, Swansea University, Swansea, Wales, UK
| | - Ernesto A B F Lima
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA
| | - Diego S Souza
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Pablo Ivan P Ramos
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
| | - Roberto F S Andrade
- Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fundação Oswaldo Cruz, Salvador, Bahia, Brazil
- Instituto de Física, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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Pinho STR, Pereira SM, Miranda JGV, Duarte TA, Nery JS, de Oliveira MG, Freitas MYGS, De Almeida NA, Moreira FB, Gomes RBC, Kerr L, Kendall C, Gomes MGM, Bessa TCB, Andrade RFS, Barreto ML. Investigating extradomiciliary transmission of tuberculosis: An exploratory approach using social network patterns of TB cases and controls and the genotyping of Mycobacterium tuberculosis. Tuberculosis (Edinb) 2020; 125:102010. [PMID: 33166778 DOI: 10.1016/j.tube.2020.102010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2020] [Revised: 09/30/2020] [Accepted: 10/12/2020] [Indexed: 11/27/2022]
Abstract
Extradomiciliary contacts have been overlooked in the study of TB transmission due to difficulties in identifying actual contacts in large populations. Complex network analysis provides a framework to model the structure of contacts, specially extradomiciliary ones. We conducted a study of incident sputum-positive TB cases and healthy controls occurring in a moderate TB burden city. Cases and controls were interviewed to obtain data regarding the usual locations of residence, work, study, and leisure. Mycobacterium tuberculosis isolated from sputum was genotyped. The collected data were used to build networks based on a framework of putative social interactions indicating possible TB transmission. A user-friendly open source environment (GraphTube) was setup to extract information from the collected data. Networks based on the likelihood of patient-patient, patient-healthy, and healthy-healthy contacts were setup, depending on a constraint of geographical distance of places attended by the volunteers. Using a threshold for the geographical distance of 300 m, the differences between TB cases and controls are revealed. Several clusters formed by social network nodes with high genotypic similarity were characterized. The developed framework provided consistent results and can be used to support the targeted search of potentially infected individuals and to help to understand the TB transmission.
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Affiliation(s)
- Suani T R Pinho
- Instituto De Física - UFBA. R. Barão De Jeremoabo, S/n. Ondina, 40170-115, Salvador, BA, Brazil.
| | - Susan M Pereira
- Instituto De Saúde Coletiva - UFBA. R. Basílio da Gama, S/n. Canela, 40110-040, Salvador, BA, Brazil.
| | - José G V Miranda
- Instituto De Física - UFBA. R. Barão De Jeremoabo, S/n. Ondina, 40170-115, Salvador, BA, Brazil.
| | - Tonya A Duarte
- Instituto De Ciências da Saúde - UFBA. Av. Reitor Miguel Calmon, S/n. Canela, 40231-300, Salvador, BA, Brazil.
| | - Joilda S Nery
- Instituto De Saúde Coletiva - UFBA. R. Basílio da Gama, S/n. Canela, 40110-040, Salvador, BA, Brazil.
| | - Maeli G de Oliveira
- Universidade Estadual De Feira De Santana. Av. Transnordestina, S/n. Novo Horizonte, 44036-900, Feira de Santana, BA, Brazil.
| | - M Yana G S Freitas
- Universidade Estadual De Feira De Santana. Av. Transnordestina, S/n. Novo Horizonte, 44036-900, Feira de Santana, BA, Brazil.
| | - Naila A De Almeida
- Serviço Nacional De Aprendizagem Industrial - SENAI. R, Henrique Dias. Roma, 40444-000, Salvador, BA, Brazil.
| | - Fabio B Moreira
- Instituto De Física - UFBA. R. Barão De Jeremoabo, S/n. Ondina, 40170-115, Salvador, BA, Brazil.
| | - Raoni B C Gomes
- Instituto De Saúde Coletiva - UFBA. R. Basílio da Gama, S/n. Canela, 40110-040, Salvador, BA, Brazil.
| | - Ligia Kerr
- Faculdade De Medicina - UFC. R. Alexandre Baraúna, 949. Rodolfo Teófilo, 60430-160, Fortaleza, CE, Brazil.
| | - Carl Kendall
- School of Public Health and Tropical Medicine Tulane University, 1440 Canal St, New Orleans, LA, 70112, United States.
| | - M Gabriela M Gomes
- Liverpool School of Tropical Medicine, Liverpool, UK, Pembroke Pl, Liverpool L3 5QA, Reino Unido, UK.
| | - Theolis C B Bessa
- Instituto Gonçalo Moniz - IGM/FIOCRUZ. R. Waldemar Falcão, 121. Candeal, 40296-710, Salvador, BA, Brazil.
| | - Roberto F S Andrade
- Instituto De Física - UFBA. R. Barão De Jeremoabo, S/n. Ondina, 40170-115, Salvador, BA, Brazil.
| | - Mauricio L Barreto
- Centro de Integração de Dados e Conhecimentos para Saúde - CIDACS/FIOCRUZ, Parque Tecnológico Edf. Tecnocentro. Rua Mundo, 121, Salvador, BA, Brazil.
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9
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Cardim LL, Pinho STR, Teixeira MG, Costa MCN, Esteva ML, Ferreira CP. Heterogeneities in dengue spatial-temporal transmission in Brazilian cities and its influence on the optimal age of vaccination. BMC Public Health 2019; 19:155. [PMID: 30727988 PMCID: PMC6364408 DOI: 10.1186/s12889-019-6426-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2018] [Accepted: 01/10/2019] [Indexed: 12/04/2022] Open
Abstract
Background The development of a safe and effective vaccine is considered crucial for dengue transmission control since vetor control has been failed; some potential candidates are currently in test, and in this context theoretical studies are necessary to evaluate vaccination strategies such as the age groups that should be vaccinated, the percentage of the population at risk, and the target geographic regions to make dengue control feasible and optimal. Methods A partial differential model is used to mimics dengue transmission in human population in order to estimate the optimal vaccination age, using data collected from dengue reported cases in ten cities of Brazil from 2001 to 2014. For this purpose, the basic reproduction number of the disease was minimized assuming a single-dose vaccination strategy, equal vaccine efficacy for all circulating serotypes, and no vaccine failure. Numerical methods were used to assess the optimal vaccination age and its confidence age range. Results The results reveal complex spatial-temporal patterns associated to the disease transmission, highlighting the heterogeneity in defining the target population for dengue vaccination. However, the values obtained for the optimal age of vaccination, as targeting individuals under 13 years old, are compatible with the ones reported in similar studies in Brazil. The results also show that the optimal age for vaccination in general does not match with the age of the highest number of cases. Conclusions The variation of the optimal age for vaccination across the country reflects heterogeneities in dengue spatial-temporal transmission in Brazilian cities, and can be used to define the target population and cities to optimize vaccination strategies in a context of high cost and low quantity of available vaccine.
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Affiliation(s)
- Luciana L Cardim
- Instituto de Saúde Coletiva, Universidade Federal da Bahia, Salvador, 40.110-140, Brazil
| | - Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia, Rua Caetano Moura, Campus Universitário de Ondina, Salvador, 40.210-340, Brazil.
| | - M Gloria Teixeira
- Instituto de Saúde Coletiva, Universidade Federal da Bahia, Salvador, 40.110-140, Brazil
| | - M Conceição N Costa
- Instituto de Saúde Coletiva, Universidade Federal da Bahia, Salvador, 40.110-140, Brazil
| | - M Lourdes Esteva
- Facultad de Ciencias, Universidad Nacional Autónoma de México, México, 04510, México
| | - Claudia P Ferreira
- São Paulo State University (UNESP), Institute of Biosciences, Department of Biostatistics, Botucatu, 18618-000, Brazil
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10
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Góes-Neto A, Diniz MVC, Carvalho DS, Bomfim GC, Duarte AA, Brzozowski JA, Petit Lobão TC, Pinho STR, El-Hani CN, Andrade RFS. Comparison of complex networks and tree-based methods of phylogenetic analysis and proposal of a bootstrap method. PeerJ 2018; 6:e4349. [PMID: 29441237 PMCID: PMC5808311 DOI: 10.7717/peerj.4349] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2017] [Accepted: 01/19/2018] [Indexed: 11/20/2022] Open
Abstract
Complex networks have been successfully applied to the characterization and modeling of complex systems in several distinct areas of Biological Sciences. Nevertheless, their utilization in phylogenetic analysis still needs to be widely tested, using different molecular data sets and taxonomic groups, and, also, by comparing complex networks approach to current methods in phylogenetic analysis. In this work, we compare all the four main methods of phylogenetic analysis (distance, maximum parsimony, maximum likelihood, and Bayesian) with a complex networks method that has been used to provide a phylogenetic classification based on a large number of protein sequences as those related to the chitin metabolic pathway and ATP-synthase subunits. In order to perform a close comparison to these methods, we selected Basidiomycota fungi as the taxonomic group and used a high-quality, manually curated and characterized database of chitin synthase sequences. This enzymatic protein plays a key role in the synthesis of one of the exclusive features of the fungal cell wall: the presence of chitin. The communities (modules) detected by the complex network method corresponded exactly to the groups retrieved by the phylogenetic inference methods. Additionally, we propose a bootstrap method for the complex network approach. The statistical results we have obtained with this method were also close to those obtained using traditional bootstrap methods.
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Affiliation(s)
- Aristóteles Góes-Neto
- Department of Microbiology, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Marcelo V C Diniz
- Department of Microbiology, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
| | - Daniel S Carvalho
- Institute of Biology, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Gilberto C Bomfim
- Institute of Biology, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Angelo A Duarte
- Department of Technology, Universidade Estadual de Feira de Santana, Feira de Santana, Bahia, Brazil
| | - Jerzy A Brzozowski
- Interdisciplinary Graduate Program in Human Sciences, Federal University of Fronteira Sul, Erechim, Rio Grande do Sul, Brazil
| | | | - Suani T R Pinho
- Institute of Physics, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Charbel N El-Hani
- Institute of Biology, Universidade Federal da Bahia, Salvador, Bahia, Brazil.,National Institute of Science & Technology in Interdisciplinary and Transdisciplinary Studies in Ecology and Evolution (IN-TREE), Instituto de Biologia, Universidade Federal da Bahia, Salvador, Bahia, Brazil
| | - Roberto F S Andrade
- Institute of Physics, Universidade Federal da Bahia, Salvador, Bahia, Brazil
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11
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Abstract
The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σβ than infection rate β). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIR_{I}^{E}) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ<1) and social contagions (σ>1).
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Affiliation(s)
- Alessandro S Barros
- Departamento de Física, Instituto Federal da Bahia-40110-150 Salvador, Brazil
| | - Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia-40210-340 Salvador, Brazil
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12
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Carvalho DS, Andrade RFS, Pinho STR, Góes-Neto A, Lobão TCP, Bomfim GC, El-Hani CN. What are the Evolutionary Origins of Mitochondria? A Complex Network Approach. PLoS One 2015; 10:e0134988. [PMID: 26332127 PMCID: PMC4557972 DOI: 10.1371/journal.pone.0134988] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2015] [Accepted: 07/15/2015] [Indexed: 11/18/2022] Open
Abstract
Mitochondria originated endosymbiotically from an Alphaproteobacteria-like ancestor. However, it is still uncertain which extant group of Alphaproteobacteria is phylogenetically closer to the mitochondrial ancestor. The proposed groups comprise the order Rickettsiales, the family Rhodospirillaceae, and the genus Rickettsia. In this study, we apply a new complex network approach to investigate the evolutionary origins of mitochondria, analyzing protein sequences modules in a critical network obtained through a critical similarity threshold between the studied sequences. The dataset included three ATP synthase subunits (4, 6, and 9) and its alphaproteobacterial homologs (b, a, and c). In all the subunits, the results gave no support to the hypothesis that Rickettsiales are closely related to the mitochondrial ancestor. Our findings support the hypothesis that mitochondria share a common ancestor with a clade containing all Alphaproteobacteria orders, except Rickettsiales.
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Affiliation(s)
- Daniel S. Carvalho
- General Biology Department, Institute of Biology, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Roberto F. S. Andrade
- General Physics Department, Institute of Physics, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Suani T. R. Pinho
- General Physics Department, Institute of Physics, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Aristóteles Góes-Neto
- Biological Sciences Department, State University of Feira de Santana, Feira de Santana, Bahia, Brazil
| | - Thierry C. P. Lobão
- Mathematics Department, Institute of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Gilberto C. Bomfim
- General Biology Department, Institute of Biology, Federal University of Bahia, Salvador, Bahia, Brazil
| | - Charbel N. El-Hani
- General Biology Department, Institute of Biology, Federal University of Bahia, Salvador, Bahia, Brazil
- * E-mail:
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Lopes JS, Rodrigues P, Pinho STR, Andrade RFS, Duarte R, Gomes MGM. Interpreting measures of tuberculosis transmission: a case study on the Portuguese population. BMC Infect Dis 2014; 14:340. [PMID: 24941996 PMCID: PMC4069091 DOI: 10.1186/1471-2334-14-340] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Accepted: 06/09/2014] [Indexed: 11/18/2022] Open
Abstract
Background Tuberculosis remains a high burden for Human society despite considerable investments in its control. Unique features in the history of infection and transmission dynamics of tuberculosis pose serious limitations on the direct interpretation of surveillance data and call for models that incorporate latent processes and simulate specific interventions. Methods A transmission model was adjusted to the dataset of active tuberculosis cases reported in Portugal between 2002 and 2009. We estimated key transmission parameters from the data (i.e. time to diagnosis, treatment length, default proportion, proportion of pulmonary TB cases). Using the adjusted model to the Portuguese case, we estimated the total burden of tuberculosis in Portugal. We further performed sensitivity analysis to heterogeneities in susceptibility to infection and exposure intensity. Results We calculated a mean time to diagnose of 2.81 months and treatment length of 8.80 months in Portugal. The proportion defaulting treatment was calculated as 0.04 and the proportion of pulmonary cases as 0.75. Using these values, we estimated a TB burden of 1.6 million infected persons, corresponding to more than 15% of the Portuguese population. We further described the sensitivity of these estimates to heterogeneity. Conclusions We showed that the model reproduces well the observed dynamics of the Portuguese data, thus demonstrating its adequacy for devising control strategies for TB and predicting the effects of interventions.
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Affiliation(s)
- Joao Sollari Lopes
- Instituto Gulbenkian de Ciência, Apartado 14, 2781-901 Oeiras, Portugal.
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14
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de Souza DR, Tomé T, Pinho STR, Barreto FR, de Oliveira MJ. Stochastic dynamics of dengue epidemics. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:012709. [PMID: 23410361 DOI: 10.1103/physreve.87.012709] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2012] [Revised: 12/06/2012] [Indexed: 05/04/2023]
Abstract
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice versa, so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible, for any death rate of infected mosquitoes.
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Affiliation(s)
- David R de Souza
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, Brazil
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15
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Andrade RFS, Rocha-Neto IC, Santos LBL, de Santana CN, Diniz MVC, Lobão TP, Goés-Neto A, Pinho STR, El-Hani CN. Detecting network communities: an application to phylogenetic analysis. PLoS Comput Biol 2011; 7:e1001131. [PMID: 21573202 PMCID: PMC3088654 DOI: 10.1371/journal.pcbi.1001131] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2010] [Accepted: 04/04/2011] [Indexed: 01/26/2023] Open
Abstract
This paper proposes a new method to identify communities in generally weighted
complex networks and apply it to phylogenetic analysis. In this case, weights
correspond to the similarity indexes among protein sequences, which can be used
for network construction so that the network structure can be analyzed to
recover phylogenetically useful information from its properties. The analyses
discussed here are mainly based on the modular character of protein similarity
networks, explored through the Newman-Girvan algorithm, with the help of the
neighborhood matrix . The most relevant
networks are found when the network topology changes abruptly revealing distinct
modules related to the sets of organisms to which the proteins belong. Sound
biological information can be retrieved by the computational routines used in
the network approach, without using biological assumptions other than those
incorporated by BLAST. Usually, all the main bacterial phyla and, in some cases,
also some bacterial classes corresponded totally (100%) or to a great
extent (>70%) to the modules. We checked for internal consistency in
the obtained results, and we scored close to 84% of matches for community
pertinence when comparisons between the results were performed. To illustrate
how to use the network-based method, we employed data for enzymes involved in
the chitin metabolic pathway that are present in more than 100 organisms from an
original data set containing 1,695 organisms, downloaded from GenBank on May 19,
2007. A preliminary comparison between the outcomes of the network-based method
and the results of methods based on Bayesian, distance, likelihood, and
parsimony criteria suggests that the former is as reliable as these commonly
used methods. We conclude that the network-based method can be used as a
powerful tool for retrieving modularity information from weighted networks,
which is useful for phylogenetic analysis. Complex weighted networks have been applied to uncover organizing principles of
complex biological, technological, and social systems. We propose herein a new
method to identify communities in such structures and apply it to phylogenetic
analysis. Recent studies using this theory in genomics and proteomics
contributed to the understanding of the structure and dynamics of cellular
complex interaction webs. Three main distinct molecular networks have been
investigated based on transcriptional and metabolic activity, and on protein
interaction. Here we consider the evolutionary relationship between proteins
throughout phylogeny, employing the complex network approach to perform a
comparative study of the enzymes related to the chitin metabolic pathway. We
show how the similarity index of protein sequences can be used for network
construction, and how the underlying structure is analyzed by the computational
routines of our method to recover useful and sound information for phylogenetic
studies. By focusing on the modular character of protein similarity networks, we
were successful in matching the identified networks modules to main bacterial
phyla, and even some bacterial classes. The network-based method reported here
can be used as a new powerful tool for identifying communities in complex
networks, retrieving useful information for phylogenetic studies.
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Affiliation(s)
- Roberto F. S. Andrade
- Institute of Physics, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
| | - Ivan C. Rocha-Neto
- Institute of Mathematics, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
| | - Leonardo B. L. Santos
- Institute of Physics, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
- National Institute for Space Research, São José dos Campos,
São Paulo, Brazil
| | - Charles N. de Santana
- Mediterranean Institute of Advanced Studies, IMEDEA (CSIC-UIB), Esporles
(Islas Baleares), Spain
| | - Marcelo V. C. Diniz
- Department of Biological Sciences, State University of Feira de Santana,
Feira de Santana, Bahia, Brazil
| | - Thierry Petit Lobão
- Institute of Mathematics, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
| | - Aristóteles Goés-Neto
- Department of Biological Sciences, State University of Feira de Santana,
Feira de Santana, Bahia, Brazil
| | - Suani T. R. Pinho
- Institute of Physics, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
| | - Charbel N. El-Hani
- Institute of Biology, Federal University of Bahia, Campus
Universitário de Ondina, Salvador, Bahia, Brazil
- * E-mail:
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16
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Pinho STR, Ferreira CP, Esteva L, Barreto FR, Morato e Silva VC, Teixeira MGL. Modelling the dynamics of dengue real epidemics. Philos Trans A Math Phys Eng Sci 2010; 368:5679-93. [PMID: 21078642 DOI: 10.1098/rsta.2010.0278] [Citation(s) in RCA: 68] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
In this work, we use a mathematical model for dengue transmission with the aim of analysing and comparing two dengue epidemics that occurred in Salvador, Brazil, in 1995-1996 and 2002. Using real data, we obtain the force of infection, Λ, and the basic reproductive number, R(0), for both epidemics. We also obtain the time evolution of the effective reproduction number, R(t), which results in a very suitable measure to compare the patterns of both epidemics. Based on the analysis of the behaviour of R(0) and R(t) in relation to the adult mosquito control parameter of the model, we show that the control applied only to the adult stage of the mosquito population is not sufficient to stop dengue transmission, emphasizing the importance of applying the control to the aquatic phase of the mosquito.
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Affiliation(s)
- S T R Pinho
- Instituto de Física, Universidade Federal da Bahia, 40210-340, Salvador, BA, Brazil.
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17
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Santos LBL, Costa MC, Pinho STR, Andrade RFS, Barreto FR, Teixeira MG, Barreto ML. Periodic forcing in a three-level cellular automata model for a vector-transmitted disease. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 80:016102. [PMID: 19658769 DOI: 10.1103/physreve.80.016102] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2008] [Revised: 03/14/2009] [Indexed: 05/28/2023]
Abstract
A periodically forced two-dimensional cellular automata model is used to reproduce and analyze the complex spatiotemporal patterns observed in the transmission of vector infectious diseases. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector-transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult, and immature vector populations. The dynamics includes external seasonality forcing, human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well-defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of the absence of external periodic drive, the model predicts a completely distinct long-time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided that the forcing term takes into account the local rainfall modulation. Finally, an analysis is provided of the effect of the dependence between epidemics threshold and vector control actions, both in the presence and absence of human mobility factor.
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Affiliation(s)
- L B L Santos
- Instituto de Física, Universidade Federal da Bahia, 40210-340 Salvador, Brazil
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18
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Andrade RFS, Pinho STR. Tsallis scaling and the long-range Ising chain: A transfer matrix approach. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 71:026126. [PMID: 15783397 DOI: 10.1103/physreve.71.026126] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2004] [Revised: 12/03/2004] [Indexed: 05/24/2023]
Abstract
A numerically efficient transfer matrix (TM) approach is introduced to investigate the long-range Ising spin chain. Results obtained within this procedure are primarily used to verify the Tsallis scaling hypothesis for long-range systems with an alpha power-law decay of the interaction constants, both in the extensive (alpha>1) and nonextensive (alpha<1) regimes. Results for finite-size systems, taking into account all interactions between spins up to 24 sites apart, show that the conjecture is satisfied with a very good precision (less than 0.004%) for all temperature intervals. This TM procedure is further used to investigate several other thermodynamic and critical properties of this system, and it may also be extended to similar one-dimensional long-range systems.
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Affiliation(s)
- R F S Andrade
- Instituto de Física, Universidade Federal da Bahia, 40210-340 Salvador, Brazil
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