Dynamic Epidemiological Models for Dengue Transmission: A Systematic Review of Structural Approaches

Dengue is a vector-borne disease recognized as the major arbovirose with four immunologically distant dengue serotypes coexisting in many endemic areas. Several mathematical models have been developed to understand the transmission dynamics of dengue, including the role of cross-reactive antibodies for the four different dengue serotypes. We aimed to review deterministic models of dengue transmission, in order to summarize the evolution of insights for, and provided by, such models, and to identify important characteristics for future model development. We identified relevant publications using PubMed and ISI Web of Knowledge, focusing on mathematical deterministic models of dengue transmission. Model assumptions were systematically extracted from each reviewed model structure, and were linked with their underlying epidemiological concepts. After defining common terms in vector-borne disease modelling, we generally categorised fourty-two published models of interest into single serotype and multiserotype models. The multi-serotype models assumed either vector-host or direct host-to-host transmission (ignoring the vector component). For each approach, we discussed the underlying structural and parameter assumptions, threshold behaviour and the projected impact of interventions. In view of the expected availability of dengue vaccines, modelling approaches will increasingly focus on the effectiveness and cost-effectiveness of vaccination options. For this purpose, the level of representation of the vector and host populations seems pivotal. Since vector-host transmission models would be required for projections of combined vaccination and vector control interventions, we advocate their use as most relevant to advice health policy in the future. The limited understanding of the factors which influence dengue transmission as well as limited data availability remain important concerns when applying dengue models to real-world decision problems.

[1]  G. Dimopoulos,et al.  Dengue Virus Infection of the Aedes aegypti Salivary Gland and Chemosensory Apparatus Induces Genes that Modulate Infection and Blood-Feeding Behavior , 2012, PLoS pathogens.

[2]  Mario Recker,et al.  Assessing the Potential of a Candidate Dengue Vaccine with Mathematical Modeling , 2012, PLoS neglected tropical diseases.

[3]  Nico Stollenwerk,et al.  The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis. , 2011, Journal of theoretical biology.

[4]  Michael B. Bonsall,et al.  A Model Framework to Estimate Impact and Cost of Genetics-Based Sterile Insect Methods for Dengue Vector Control , 2011, PloS one.

[5]  M. G. Castro,et al.  Potential impact of a presumed increase in the biting activity of dengue-virus-infected Aedes aegypti (Diptera: Culicidae) females on virus transmission dynamics. , 2011, Memorias do Instituto Oswaldo Cruz.

[6]  Michael A. Johansson,et al.  Models of the impact of dengue vaccines: a review of current research and potential approaches. , 2011, Vaccine.

[7]  D. Clements,et al.  Dengue vaccines: progress and challenges. , 2011, Current opinion in immunology.

[8]  Jan Medlock,et al.  Dengue vector control strategies in an urban setting: an economic modelling assessment , 2011, The Lancet.

[9]  S. Tong,et al.  Dengue transmission in the Asia‐Pacific region: impact of climate change and socio‐environmental factors , 2011, Tropical medicine & international health : TM & IH.

[10]  Tiago Botari,et al.  Explaining the high number of infected people by dengue in Rio de Janeiro in 2008 using a susceptible-infective-recovered model. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. G. Castro,et al.  Dengue Infection Increases the Locomotor Activity of Aedes aegypti Females , 2011, PloS one.

[12]  D H Barmak,et al.  Dengue epidemics and human mobility. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  W. V. de Souza,et al.  Modeling the Dynamic Transmission of Dengue Fever: Investigating Disease Persistence , 2011, PLoS neglected tropical diseases.

[14]  M. Teixeira,et al.  Modelling the dynamics of dengue real epidemics , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  Kevin R. Long,et al.  A dengue model with a dynamic Aedes albopictus vector population , 2010 .

[16]  Kuldeep Kumar,et al.  Dengue: epidemiology, prevention and pressing need for vaccine development , 2010 .

[17]  Mario Recker,et al.  Viral and Epidemiological Determinants of the Invasion Dynamics of Novel Dengue Genotypes , 2010, PLoS neglected tropical diseases.

[18]  Mary E. Wilson,et al.  Dengue and chikungunya infections in travelers , 2010, Current opinion in infectious diseases.

[19]  Mario Recker,et al.  The Effects of Tertiary and Quaternary Infections on the Epidemiology of Dengue , 2010, PloS one.

[20]  Kevin R. Long,et al.  A stage-structured, Aedes albopictus population model , 2010 .

[21]  T. Scott,et al.  Consequences of the Expanding Global Distribution of Aedes albopictus for Dengue Virus Transmission , 2010, PLoS neglected tropical diseases.

[22]  Durrell D. Kapan,et al.  Epidemic dynamics revealed in dengue evolution. , 2010, Molecular biology and evolution.

[23]  B. Adams,et al.  How important is vertical transmission in mosquitoes for the persistence of dengue? Insights from a mathematical model. , 2010, Epidemics.

[24]  Hirofumi Ishikawa,et al.  A dengue transmission model in Thailand considering sequential infections with all four serotypes. , 2009, Journal of infection in developing countries.

[25]  S. Halstead.  Antibodies Determine Virulence in Dengue , 2009, Annals of the New York Academy of Sciences.

[26]  S. Ramchurn,et al.  An analysis of a short-lived outbreak of dengue fever in Mauritius. , 2009, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[27]  S. Bianco,et al.  Asymmetry in the Presence of Migration Stabilizes Multistrain Disease Outbreaks , 2009, Bulletin of mathematical biology.

[28]  A. Keller,et al.  The risk of dengue transmission by blood during a 2004 outbreak in Cairns, Australia , 2009, Transfusion.

[29]  Mario Recker,et al.  Immunological serotype interactions and their effect on the epidemiological pattern of dengue , 2009, Proceedings of the Royal Society B: Biological Sciences.

[30]  Samuel Bowong,et al.  Lyapunov functions for a dengue disease transmission model , 2009 .

[31]  J. Medlock,et al.  Impact of insecticide interventions on the abundance and resistance profile of Aedes aegypti , 2009, Epidemiology and Infection.

[32]  Eduardo Massad,et al.  Threat of Dengue to Blood Safety in Dengue-Endemic Countries , 2009, Emerging infectious diseases.

[33]  Ira B Schwartz,et al.  Epidemics with multistrain interactions: the interplay between cross immunity and antibody-dependent enhancement. , 2008, Chaos.

[34]  Asep K. Supriatna,et al.  A two-age-classes dengue transmission model. , 2008, Mathematical biosciences.

[35]  R F S Andrade,et al.  Periodic forcing in a three-level cellular automata model for a vector-transmitted disease. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  H. Yang,et al.  Describing the geographic spread of dengue disease by traveling waves. , 2008, Mathematical biosciences.

[37]  Salisu M. Garba,et al.  Backward bifurcations in dengue transmission dynamics. , 2008, Mathematical biosciences.

[38]  Xue-Zhi Li,et al.  An epidemic model of a vector-borne disease with direct transmission and time delay , 2008 .

[39]  Stefan Ma,et al.  The risk of chikungunya fever in a dengue-endemic area. , 2008, Journal of travel medicine.

[40]  Hyun Mo Yang,et al.  Assessing the effects of vector control on dengue transmission , 2008, Appl. Math. Comput..

[41]  G. Perng,et al.  Alternate Hypothesis on the Pathogenesis of Dengue Hemorrhagic Fever (DHF)/Dengue Shock Syndrome (DSS) in Dengue Virus Infection , 2008, Experimental biology and medicine.

[42]  B. Angel,et al.  Distribution and seasonality of vertically transmitted dengue viruses in Aedes mosquitoes in arid and semi-arid areas of Rajasthan, India. , 2008, Journal of vector borne diseases.

[43]  H. Solari,et al.  A Stochastic Spatial Dynamical Model for Aedes Aegypti , 2008, Bulletin of mathematical biology.

[44]  Katia Koelle,et al.  Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever , 2008, Proceedings of the National Academy of Sciences.

[45]  Eduardo Massad,et al.  Scale-free network of a dengue epidemic , 2008, Appl. Math. Comput..

[46]  I. Schwartz,et al.  Vaccinations in disease models with antibody-dependent enhancement. , 2008, Mathematical biosciences.

[47]  James Watmough,et al.  Role of incidence function in vaccine-induced backward bifurcation in some HIV models. , 2007, Mathematical biosciences.

[48]  Richard G Jarman,et al.  Analysis of repeat hospital admissions for dengue to estimate the frequency of third or fourth dengue infections resulting in admissions and dengue hemorrhagic fever, and serotype sequences. , 2007, The American journal of tropical medicine and hygiene.

[49]  B. Tyagi,et al.  Natural vertical transmission of dengue virus in Aedes albopictus (Diptera: Culicidae) in Kerala, a southern Indian state. , 2007, Japanese journal of infectious diseases.

[50]  J. Hyman,et al.  Estimation of the reproduction number of dengue fever from spatial epidemic data. , 2007, Mathematical biosciences.

[51]  B. Murphy,et al.  Prospects for a dengue virus vaccine , 2007, Nature Reviews Microbiology.

[52]  E Massad,et al.  Modelling the control strategies against dengue in Singapore , 2007, Epidemiology and Infection.

[53]  Lawrence M. Wein,et al.  Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system , 2007, Proceedings of the National Academy of Sciences.

[54]  Ira B Schwartz,et al.  Instabilities in multiserotype disease models with antibody-dependent enhancement. , 2007, Journal of theoretical biology.

[55]  Roberto Barrera,et al.  Habitat segregation of dengue vectors along an urban environmental gradient. , 2007, The American journal of tropical medicine and hygiene.

[56]  I-Ming Tang,et al.  Destabilizing effect of the host immune status on the sequential transmission dynamic of the dengue virus infection , 2007, Math. Comput. Model..

[57]  M. L. Martins,et al.  Epidemic spreading in a scale-free network of regular lattices , 2007 .

[58]  L. P. Lounibos,et al.  Spread of the tiger: global risk of invasion by the mosquito Aedes albopictus. , 2007, Vector borne and zoonotic diseases.

[59]  Ben Adams,et al.  Modelling the relationship between antibody-dependent enhancement and immunological distance with application to dengue. , 2006, Journal of theoretical biology.

[60]  E Massad,et al.  Threshold Conditions for a Non-Autonomous Epidemic System Describing the Population Dynamics of Dengue , 2006, Bulletin of mathematical biology.

[61]  Pejman Rohani,et al.  Ecological and immunological determinants of dengue epidemics. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[62]  H. Solari,et al.  A Stochastic Population Dynamics Model for Aedes Aegypti: Formulation and Application to a City with Temperate Climate , 2006, Bulletin of mathematical biology.

[63]  Jacqueline L Deen,et al.  The WHO dengue classification and case definitions: time for a reassessment , 2006, The Lancet.

[64]  Mohammed Derouich,et al.  Dengue fever: Mathematical modelling and computer simulation , 2006, Appl. Math. Comput..

[65]  T. Jelínek,et al.  Dengue in travelers: a review. , 2006, Journal of travel medicine.

[66]  C. Favier,et al.  Early determination of the reproductive number for vector‐borne diseases: the case of dengue in Brazil , 2006, Tropical medicine & international health : TM & IH.

[67]  Ira B Schwartz,et al.  Dynamic effects of antibody-dependent enhancement on the fitness of viruses. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[68]  Charly Favier,et al.  Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics , 2005, Proceedings of the Royal Society B: Biological Sciences.

[69]  Petronio Pulino,et al.  Mathematical models for the Aedes aegypti dispersal dynamics: Travelling waves by wing and wind , 2005, Bulletin of mathematical biology.

[70]  D. Cummings,et al.  Chaotic desynchronization of multistrain diseases. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  D. Guha-Sapir,et al.  Dengue fever: new paradigms for a changing epidemiology , 2005, Emerging themes in epidemiology.

[72]  E. Massad,et al.  An approximate threshold condition for non-autonomous system: An application to a vector-borne infection , 2005, Math. Comput. Simul..

[73]  G. Malavige,et al.  Dengue viral infections , 2004, Postgraduate Medical Journal.

[74]  Mary E. Wilson,et al.  Transmission of dengue virus without a mosquito vector: nosocomial mucocutaneous transmission and other routes of transmission. , 2004, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[75]  N. Gratz,et al.  Critical review of the vector status of Aedes albopictus , 2004, Medical and veterinary entomology.

[76]  Sasithon Pukrittayakamee,et al.  Risk factors and clinical features associated with severe dengue infection in adults and children during the 2001 epidemic in Chonburi, Thailand , 2004, Tropical medicine & international health : TM & IH.

[77]  G. Krause,et al.  Increase in Imported Dengue, Germany, 2001–2002 , 2004, Emerging infectious diseases.

[78]  K. Patanarapelert,et al.  Infection risk to travelers going to dengue fever endemic regions. , 2004, The Southeast Asian journal of tropical medicine and public health.

[79]  R. Irizarry,et al.  Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand , 2004, Nature.

[80]  Akira Sasaki,et al.  Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[81]  Eduardo Massad,et al.  Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil. , 2003, Revista de saude publica.

[82]  D. Gubler,et al.  Emergence and Global Spread of a Dengue Serotype 3, Subtype III Virus , 2003, Emerging infectious diseases.

[83]  Edward C Holmes,et al.  The origin, emergence and evolutionary genetics of dengue virus. , 2003, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[84]  P. Pongsumpun,et al.  Transmission of dengue hemorrhagic fever in an age structured population , 2003 .

[85]  J. Lindbäck,et al.  Dengue Fever in Travelers to the Tropics, 1998 and 1999 , 2003, Emerging infectious diseases.

[86]  N. Mühlberger,et al.  Epidemiology and clinical features of imported dengue fever in Europe: sentinel surveillance data from TropNetEurop. , 2002, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[87]  R. Sharma,et al.  Persistence of dengue-3 virus through transovarial transmission passage in successive generations of Aedes aegypti mosquitoes. , 2002, The American journal of tropical medicine and hygiene.

[88]  C. Donnelly,et al.  The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms. , 2002, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[89]  S. Halstead,et al.  Effect of age on outcome of secondary dengue 2 infections. , 2002, International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases.

[90]  L. Alphey,et al.  Dominant lethality and insect population control. , 2002, Molecular and biochemical parasitology.

[91]  D. Gubler.  Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century. , 2002, Trends in microbiology.

[92]  M. Takagi,et al.  Survival and Development of Aedes aegypti and Aedes albopictus (Diptera: Culicidae) Larvae Under a Seasonally Changing Environment in Nagasaki, Japan , 2001 .

[93]  Chung Youne Kow,et al.  Detection of Dengue Viruses in Field Caught Male Aedes aegypti and Aedes albopictus (Diptera: Culicidae) in Singapore by Type-Specific PCR , 2001, Journal of medical entomology.

[94]  E Massad,et al.  The risk of yellow fever in a dengue-infested area. , 2001, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[95]  I. M. Rocco,et al.  First isolation of dengue 3 in Brazil from an imported case. , 2001, Revista do Instituto de Medicina Tropical de Sao Paulo.

[96]  I. Kurane,et al.  Trends in flavivirus infections in Japan. , 2000, Emerging infectious diseases.

[97]  D. Vaughn.  Invited commentary: Dengue lessons from Cuba. , 2000, American journal of epidemiology.

[98]  R. Manavalan,et al.  Natural vertical transmission of dengue viruses in Aedes aegypt in southern India. , 2000, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[99]  L. Esteva,et al.  Influence of vertical and mechanical transmission on the dynamics of dengue disease. , 2000, Mathematical biosciences.

[100]  T. Jelínek,et al.  Dengue fever in international travelers. , 2000, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[101]  W. J. McBride,et al.  Dengue viral infections; pathogenesis and epidemiology. , 2000, Microbes and infection.

[102]  N M Ferguson,et al.  Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[103]  N. Ferguson,et al.  The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[104]  D. Gubler,et al.  Dengue and Dengue Hemorrhagic Fever , 1998, Clinical Microbiology Reviews.

[105]  L. Esteva,et al.  Analysis of a dengue disease transmission model. , 1998, Mathematical biosciences.

[106]  M. Robinson,et al.  Dengue virus infection: epidemiology, pathogenesis, clinical presentation, diagnosis, and prevention. , 1997, The Journal of pediatrics.

[107]  D. Vaughn,et al.  Impact of dengue virus infection on feeding behavior of Aedes aegypti. , 1997, The American journal of tropical medicine and hygiene.

[108]  J. Velasco-Hernández,et al.  Competitive exclusion in a vector-host model for the dengue fever , 1997, Journal of mathematical biology.

[109]  D. Gubler,et al.  Community involvement in the control of Aedes aegypti. , 1996, Acta tropica.

[110]  D. Focks,et al.  A simulation model of the epidemiology of urban dengue fever: literature analysis, model development, preliminary validation, and samples of simulation results. , 1995, The American journal of tropical medicine and hygiene.

[111]  T. Scott,et al.  Blood-feeding behavior of dengue-2 virus-infected Aedes aegypti. , 1995, The American journal of tropical medicine and hygiene.

[112]  Scott M. Hanson,et al.  Cold acclimation, diapause, and geographic origin affect cold hardiness in eggs of Aedes albopictus (Diptera: Culicidae). , 1994, Journal of medical entomology.

[113]  N. Grist,et al.  Aedes and dengue , 1994, The Lancet.

[114]  D. Focks,et al.  Dynamic life table model for Aedes aegypti (Diptera: Culicidae): analysis of the literature and model development. , 1993, Journal of medical entomology.

[115]  H. Schatzmayr,et al.  Dengue epidemic in the state of Rio de Janeiro, Brazil, 1990–1: co-circulation of dengue 1 and dengue 2 serotypes , 1993, Epidemiology and Infection.

[116]  N. Grist.  Aedes albopictus: the tyre-travelling tiger. , 1993, The Journal of infection.

[117]  P. Reiter,et al.  A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics. , 1992, The American journal of tropical medicine and hygiene.

[118]  Tom Starzl,et al.  THE LANCET , 1992, The Lancet.

[119]  I M Longini,et al.  Determinants and predictors of dengue infection in Mexico. , 1991, American journal of epidemiology.

[120]  B. Miller,et al.  Vertical transmission of dengue viruses by strains of Aedes albopictus recently introduced into Brazil. , 1990, Journal of the American Mosquito Control Association.

[121]  M. Guzmán,et al.  Dengue hemorrhagic fever in Cuba, 1981: a retrospective seroepidemiologic study. , 1990, The American journal of tropical medicine and hygiene.

[122]  A. Nisalak,et al.  Antibody-dependent enhancement of dengue virus growth in human monocytes as a risk factor for dengue hemorrhagic fever. , 1989, The American journal of tropical medicine and hygiene.

[123]  A. Spielman,et al.  Increased biting rate and reduced fertility in sporozoite-infected mosquitoes. , 1986, The American journal of tropical medicine and hygiene.

[124]  S. Halstead,et al.  Risk factors in dengue shock syndrome: a prospective epidemiologic study in Rayong, Thailand. I. The 1980 outbreak. , 1984, American journal of epidemiology.

[125]  Christopher Dye,et al.  Models for the population dynamics of the yellow fever mosquito, Aedes aegypti , 1984 .

[126]  R. Tesh,et al.  Transovarial transmission of dengue viruses by mosquitoes: Aedes albopictus and Aedes aegypti. , 1983, The American journal of tropical medicine and hygiene.

[127]  M. Khin,et al.  Transovarial transmission of dengue 2 virus by Aedes aegypti in nature. , 1983, The American journal of tropical medicine and hygiene.

[128]  J. S. Porterfield.  Immunological enhancement and the pathogenesis of dengue haemorrhagic fever , 1982, Journal of Hygiene.

[129]  G B Craig,et al.  Aedes triseriatus (Diptera: Culicidae) and La Crosse virus. II. Modification of mosquito feeding behavior by virus infection. , 1980, Journal of medical entomology.

[130]  N. Ling.  The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[131]  S. Halstead,et al.  Immunological enhancement of dengue virus replication. , 1973, Nature: New biology.

[132]  P. M. Sheppard,et al.  The dynamics of an adult population of Aedes aegypti in relation to dengue haemorrhagic fever in Bangkok. , 1969 .

[133]  S. Halstead,et al.  Dengue , 1872, The Lancet.

[134]  D. Gubler,et al.  Dengue and dengue hemorrhagic fever. , 2014 .

[135]  H G Solari,et al.  Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito. , 2010, Mathematical biosciences.

[136]  M. Guzmán,et al.  Secondary heterologous dengue infection risk: Disequilibrium between immune regulation and inflammation? , 2010, Cellular immunology.

[137]  Ying-Hen Hsieh,et al.  Intervention measures, turning point, and reproduction number for dengue, Singapore, 2005. , 2009, The American journal of tropical medicine and hygiene.

[138]  Asep K. Supriatna.  Estimating the basic reproduction number of dengue transmission during 2002-2007 outbreaks in Bandung, Indonesia , 2009 .

[139]  K. A. Sidarto.  Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment , 2008 .

[140]  Bob W. Kooi,et al.  Epidemiology of Dengue Fever: A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions , 2008 .

[141]  Nuning Nuraini,et al.  Mathematical Model of Dengue Disease Transmission with Severe DHF Compartment , 2007 .

[142]  Hiroshi Nishiura,et al.  Mathematical and statistical analyses of the spread of dengue , 2006 .

[143]  Lourdes Esteva,et al.  Coexistence of different serotypes of dengue virus , 2003, Journal of mathematical biology.

[144]  K. Yoon,et al.  Antibody-dependent enhancement of virus infection and disease. , 2003, Viral immunology.

[145]  M. Guzmán,et al.  Dengue: an update. , 2002, The Lancet. Infectious diseases.

[146]  D. Focks,et al.  Transmission thresholds for dengue in terms of Aedes aegypti pupae per person with discussion of their utility in source reduction efforts. , 2000, The American journal of tropical medicine and hygiene.

[147]  Lourdes Esteva,et al.  A model for dengue disease with variable human population , 1999, Journal of mathematical biology.

[148]  M. Guzmán,et al.  Reemergence of dengue in Cuba: a 1997 epidemic in Santiago de Cuba. , 1998, Emerging infectious diseases.

[149]  G. Kuno,et al.  Review of the factors modulating dengue transmission. , 1995, Epidemiologic reviews.

[150]  E. Massad,et al.  The basic reproduction number for dengue fever in São Paulo state, Brazil: 1990-1991 epidemic. , 1994, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[151]  M. Guzmán,et al.  Dengue haemorrhagic fever/dengue shock syndrome: lessons from the Cuban epidemic, 1981. , 1989, Bulletin of the World Health Organization.

[152]  B. A. Harrison,et al.  Effect of temperature on the vector efficiency of Aedes aegypti for dengue 2 virus. , 1987, The American journal of tropical medicine and hygiene.

[153]  Alexander Grey,et al.  The Mathematical Theory of Infectious Diseases and Its Applications , 1977 .

[154]  R. Tonn,et al.  Studies on the life budget of Aedes aegypti in Wat Samphaya, Bangkok, Thailand. , 1972, Bulletin of the World Health Organization.

[155]  R. Tonn,et al.  A study of biting habits of Aedes aegypti in Bangkok, Thailand. , 1970, Bulletin of the World Health Organization.

[156]  W. Hammon,et al.  New hemorrhagic fevers of children in the Philippines and Thailand. , 1960, Transactions of the Association of American Physicians.

[157]  A. Sabin.  Research on dengue during World War II. , 1952, The American journal of tropical medicine and hygiene.