- Diego Fernando Aranda Lozano
Laboratorio Distrital de Salud Pública.
Edificio LSP, 3ª planta
Secretaria de Salud Pública Bogotá D.C, 742 Bogotá D.C. - Colombia
Diego Fernando Aranda Lozano
Universidad Politécnica de Valencia, Matemáticas Aplicadas, Department Member
- Mathematical Models with Applications in the Epidemiologic, Modelos Matemáticos Aplicados a la Epidemiología, Modelos Matemáticos Aplicados a Epidemiología, Parasitología, Toxoplasmosis, Stochastic Dynamic Modeling, and 7 moreVirology, Parasitology, Mathematical Modelling, Influenza A H1N1, Academic Poster Development & Innovation, Biotechnology, and Molecular Biologyedit
- Abstract As the complexity of the world in which we live increases, system thinking is becoming a major factor in suc... moreAbstract
As the complexity of the world in which we live increases, system thinking is becoming a major factor in success and even in survival. This is why robust tools of complex dynamic systems can give answers to several problems and can be applied to many different areas, such as business, society and ecosystems, as well as in ordinary life such as compulsive shopping, drug abuse, tobacco addiction, obesity, etc. When experiments to test the real world cannot be carried out, simulation becomes the best way to learn about the dynamic of these systems. For this reason I am pleased to present this Ph.D. Dissertation, in which theory and practice of the dynamic systems are combined. It also embraces epidemiologic models of some parasitic diseases with transmission vector. The Toxoplasmosis and the bovine Babesiosis are parasitic diseases (zoonoses), which are spread through a transmission vector and a ect both human beings and livestock. As a public health problem, Toxoplasmosis causes high health care costs when treating unborn and newborn babies. It also causes a great amount of sick leaves. In addition to this, livestock economic sector in tropical countries, such as Colombia, must bear an extra cost of millions of dollars due to the high mortality rates and to the low productivity levels in by-products of farming. Mathematical models try to describe and represent reality using mathematical techniques. The importance of mathematical modeling when studying the way some diseases can spread lies in forecasting the behavior of these biological phenomena and their effects wherever they may occur. Thus mathematical models supply a valuable tool for doctors to use for containment methods, estimation and safety, as well as many other different decisions aimed to reduce economic costs. Three mathematical models, which describe the behavior of two parasitic diseases with transmission vector, are presented in this dissertation. Two of these models are dedicated to Toxoplasmosis and they explore the dynamic of the disease in relation to human population and pet cats. In this model, cats play the role of infectious agents and carrier of the protozoan Toxoplasma Gondii. The qualitative dynamic of the model is established by the basic reproduction threshold R0. If the parameter R0 < 1, then the solution converges to the equilibrium point disease free. However, if R0 > 1, convergence leads to the equilibrium point endemic. Numerical simulations of the models illustrate different dynamics according to the threshold parameter R0 and show the importance of this parameter. Finally, bovine babesiosis is modeled starting from a mathematical model, which is composed of ordinary differential equations that explain the in uence of the epidemiological parameters over the evolution of the disease. The stationary states of the system and the basic reproduction number R0 are determined. The existence of the endemic point and the disease free point are calculated and they depend on the threshold parameter R0, which determines the local and global stability of the equilibrium points.edit
ABSTRACT An AISI 304 austenitic stainless steel square bar, with a length to thickness ratio 5:1 was heated at 900°C and spray quenched with water using 4 full oval nozzles. Five thermocouples were placed in the probe to record the... more
ABSTRACT An AISI 304 austenitic stainless steel square bar, with a length to thickness ratio 5:1 was heated at 900°C and spray quenched with water using 4 full oval nozzles. Five thermocouples were placed in the probe to record the cooling time-temperature curves. Three were placed at mid-thickness plane, being one in the geometric centre, and the other thermocouples were placed 1/4 thickness and near surface (1 mm). In addition, another two thermocouples were placed in a 45° plane (diagonal from center to square edge), one at 1/2 diagonal and the other near the surface (1 mm from two surfaces in the diagonal, at mm from the square edge). The thermocouples were placed at mid-length in order to ignore the end-cooling effects and to facilitate the computation with 1D heat transfer. In addition, the square edge cooling effect was analyzed. FEM was used to model the transient temperature distribution during cooling. It was found that the cooling rate at the square edge was a factor of 1.5 greater than the cooling rate at the surface of the center of the flat face. The distance from the edge that is affected was determined.
We propose that stem cell therapy may be a potent treatment for metastatic melanoma in the brain. Here we discuss the key role of a leaky blood‐brain barrier (BBB) that accompanies the development of brain metastases. We review the need... more
We propose that stem cell therapy may be a potent treatment for metastatic melanoma in the brain. Here we discuss the key role of a leaky blood‐brain barrier (BBB) that accompanies the development of brain metastases. We review the need to characterize the immunological and inflammatory responses associated with tumor-derived BBB damage in order to reveal the contribution of this brain pathological alteration to the formation and growth of brain metastatic cancers. Next, we discuss the potential repair of the BBB and attenuation of brain metastasis through transplantation of bone marrow-derived mesenchymal stem cells with the endothelial progenitor cell phenotype. In particular, we review the need for evaluation of the efficacy of stem cell therapy in repairing a disrupted BBB in an effort to reduce neuroinflammation, eventually attenuating brain metastatic cancers. The demonstration of BBB repair through augmented angiogenesis and vasculogenesis will be critical to establishing the...
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Traumatic brain injury (TBI) is a serious public health problem accounting for 1.4 million emergency room visits by US citizens each year. Although TBI has been traditionally considered an acute injury, chronic symptoms reminiscent of... more
Traumatic brain injury (TBI) is a serious public health problem accounting for 1.4 million emergency room visits by US citizens each year. Although TBI has been traditionally considered an acute injury, chronic symptoms reminiscent of neurodegenerative disorders have now been recognized. These progressive neurodegenerative-like symptoms manifest as impaired motor and cognitive skills, as well as stress, anxiety, and mood affective behavioral alterations. TBI, characterized by external bumps or blows to the head exceeding the brain's protective capacity, causes physical damage to the central nervous system with accompanying neurological dysfunctions. The primary impact results in direct neural cell loss predominantly exhibiting necrotic death, which is then followed by a wave of secondary injury cascades including excitotoxicity, oxidative stress, mitochondrial dysfunction, blood-brain barrier disruption, and inflammation. All these processes exacerbate the damage, worsen the cli...
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Delivery of melatonin and targeting melatonin receptors pose as neuroprotective strategies for stroke therapy. The potential of melatonin--based therapeutics for clinical application in stroke patients requires translational research to... more
Delivery of melatonin and targeting melatonin receptors pose as neuroprotective strategies for stroke therapy. The potential of melatonin--based therapeutics for clinical application in stroke patients requires translational research to guide the conduct of clinical trials. We review recent preclinical and clinical data that support the use of melatonin for stroke.
Research Interests:
Research Interests:
ABSTRACT The Wharton’s jelly (WJ) of the umbilical cord has been identified as a rich source of mesenchymal stromal cells (MSCs), which are considered as promising candidates for stem cell-based therapy to treat several diseases. In... more
ABSTRACT The Wharton’s jelly (WJ) of the umbilical cord has been identified as a rich source of mesenchymal stromal cells (MSCs), which are considered as promising candidates for stem cell-based therapy to treat several diseases. In particular, MSCs harvested from the “young” WJ are believed to be more proliferative, immunosuppressive and therapeutically active stem cells than those derived from adult tissues, such as the bone marrow or adipose. MSCs derived from WJ also exhibit transplantable features such as ease of sourcing, in vitro expandability, differentiation capacities, immune-evasion and immune-regulation profiles. Indeed, the potentiality of WJ-derived stem cells to treat cancer, cardiovascular and liver diseases, and nerve and cartilage tendon injuries has been suggested. In this paper, we present an overview of the phenotypic characteristics, immune-modulatory properties and therapeutic potentials of WJ-derived stem cells, and suggest optimization protocols for successful advancement of WJ-derived stem cells into clinical use.
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Cell therapy now constitutes an important area of regenerative medicine. The aging of the population has mandated the discovery and development of new and innovative therapeutic modalities to combat devastating disorders such as stroke.... more
Cell therapy now constitutes an important area of regenerative medicine. The aging of the population has mandated the discovery and development of new and innovative therapeutic modalities to combat devastating disorders such as stroke. Menstrual blood and Sertoli cells represent two sources of viable transplantable cells that are gender-specific, both of which appear to have potential as donor cells for transplantation in stroke. During the subacute phase of stroke, the use of autologous cells offers effective and practical clinical application and is suggestive of the many benefits of using the aforementioned gender-specific cells. For example, in addition to being exceptionally immunosuppressive, testis-derived Sertoli cells secrete many growth and trophic factors and have been shown to aid in the functional recovery of animals transplanted with fetal dopaminergic cells. Correspondingly, menstrual blood cells are easily obtainable and exhibit angiogenic characteristics, prolifera...
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Introducción El virus respiratorio sincitial es uno de los principales causantes de mortalidad de niñosy adultos mayores en el mundo.Objetivo.Predecir la semana de inicio del brote del virus respiratorio sincitial en Bogotá utilizando... more
Introducción
El virus respiratorio sincitial es uno de los principales causantes de mortalidad de niñosy adultos mayores en el mundo.Objetivo.Predecir la semana de inicio del brote del virus respiratorio sincitial en Bogotá utilizando variables climatológicas como variables de predicción.
Materiales y métodos
Las fechas de inicio de la epidemias para niños menores de cinco años correspondientes al periodo 2005-2010, fueron obtenidos para la ciudad de Bogotá D.C., Colombia. Se seleccionaron las variables climatológicas utilizando la matriz de correlación y posteriormente se construyeron 1.020 modelos resultantes de combinar las distintas variables climatológicas y modelos con distintas semanas de anticipación al inicio del brote. Adicionalmente, se seleccionaron modelos utilizando datos de los periodos de seis años (2005-2010), cuatro años (2005-2008) y dos años (2009-2010). Utilizando los clasificadores de Naïve Bayes y la curvacaracterística de operación del receptor(ROC)se logródeterminar los mejores modelos y las variables climatológicas más relevantes.
Resultados
Los modelos que utilizaron el periodo de 2 años (2009-2010) y los de la semana 0, fueron los que tuvieron mejores resultados con un 52%y 60% de aciertos respectivamente. La humedad mínima fue la variable que másapareció en los mejores modelos con un 62%. Los clasificadores de Naïve Bayes permitieron establecer cuáles son los mejores modelos para predecir la semana de inicio del brote.
Conclusiones
Los resultados sugieren que los modelos que utilizan la humedad mínima, velocidad del viento y temperatura mínima son los que tienen el mayor potencial para ser utilizado como eficaces modelos predictivos.
Palabras clave:
teorema de Bayes, virus sincitialesrespiratorios, predicción, climatología, epidemias
El virus respiratorio sincitial es uno de los principales causantes de mortalidad de niñosy adultos mayores en el mundo.Objetivo.Predecir la semana de inicio del brote del virus respiratorio sincitial en Bogotá utilizando variables climatológicas como variables de predicción.
Materiales y métodos
Las fechas de inicio de la epidemias para niños menores de cinco años correspondientes al periodo 2005-2010, fueron obtenidos para la ciudad de Bogotá D.C., Colombia. Se seleccionaron las variables climatológicas utilizando la matriz de correlación y posteriormente se construyeron 1.020 modelos resultantes de combinar las distintas variables climatológicas y modelos con distintas semanas de anticipación al inicio del brote. Adicionalmente, se seleccionaron modelos utilizando datos de los periodos de seis años (2005-2010), cuatro años (2005-2008) y dos años (2009-2010). Utilizando los clasificadores de Naïve Bayes y la curvacaracterística de operación del receptor(ROC)se logródeterminar los mejores modelos y las variables climatológicas más relevantes.
Resultados
Los modelos que utilizaron el periodo de 2 años (2009-2010) y los de la semana 0, fueron los que tuvieron mejores resultados con un 52%y 60% de aciertos respectivamente. La humedad mínima fue la variable que másapareció en los mejores modelos con un 62%. Los clasificadores de Naïve Bayes permitieron establecer cuáles son los mejores modelos para predecir la semana de inicio del brote.
Conclusiones
Los resultados sugieren que los modelos que utilizan la humedad mínima, velocidad del viento y temperatura mínima son los que tienen el mayor potencial para ser utilizado como eficaces modelos predictivos.
Palabras clave:
teorema de Bayes, virus sincitialesrespiratorios, predicción, climatología, epidemias
Research Interests:
Research Interests:
Research Interests:
Objectives Describing the behavior of A H1N1/09 virus with variables of: time, age and sex; in patients with suspected infection, medical health care and laboratory diagnosis. Method Descriptive and retrospective study of patients... more
Objectives Describing the behavior of A H1N1/09 virus with variables of: time, age and sex; in patients with suspected infection, medical health care and laboratory diagnosis.
Method Descriptive and retrospective study of patients diagnosed with influenza A H1N1/09 virus, between April 2009 and July 2010 made in the Laboratory of Public Health of Bogotá D. C.
Results The first cases of A H1N1/09 virus were confirmed, since Week 17 of 2009, the positivity increased gradually, to express its maximum expression between weeks 31-36, 2009 (43 % a 53 %) and decreased in the 37th week. The age groups most affected were those of 6-15 years (35.4 %) and 16-25 years (28 %) (p=0.0044), the lowest proportions were found in children under 1 year (8.7 %) and higher to 65 years (7.2 %) (Chi 1.98, p = 0.119). The sex ratio was similar: female (18.6 %) and male (17.6 %) (Chi 1.82, p = 0.1768).
Conclusions In the year 2009, the Influenza A virus showed a significant increase of cases. However, did not alter the behavior of the endemic Respiratory Syncytial Virus, on the other hand, the subtype H1N1/09 replaced the seasonal virus that circulating in among the population of the Bogotá D.C., and similarly affected men and women, mainly young adults. The highest prevalence of cases occurred between August and September 2009.
Key Words: Influenza human, Influenza A virus, Respiratory Tract Infections, Epidemiologic Surveillance, Respiratory Syncytial Viruses, Public Health (source: MeSH, NLM).
Method Descriptive and retrospective study of patients diagnosed with influenza A H1N1/09 virus, between April 2009 and July 2010 made in the Laboratory of Public Health of Bogotá D. C.
Results The first cases of A H1N1/09 virus were confirmed, since Week 17 of 2009, the positivity increased gradually, to express its maximum expression between weeks 31-36, 2009 (43 % a 53 %) and decreased in the 37th week. The age groups most affected were those of 6-15 years (35.4 %) and 16-25 years (28 %) (p=0.0044), the lowest proportions were found in children under 1 year (8.7 %) and higher to 65 years (7.2 %) (Chi 1.98, p = 0.119). The sex ratio was similar: female (18.6 %) and male (17.6 %) (Chi 1.82, p = 0.1768).
Conclusions In the year 2009, the Influenza A virus showed a significant increase of cases. However, did not alter the behavior of the endemic Respiratory Syncytial Virus, on the other hand, the subtype H1N1/09 replaced the seasonal virus that circulating in among the population of the Bogotá D.C., and similarly affected men and women, mainly young adults. The highest prevalence of cases occurred between August and September 2009.
Key Words: Influenza human, Influenza A virus, Respiratory Tract Infections, Epidemiologic Surveillance, Respiratory Syncytial Viruses, Public Health (source: MeSH, NLM).
In this paper we analyse the Babesiosis transmission dynamics on bovines and ticks populations. Ticks play a role of infectious agents and vector of the protozoan Babesia hemo-parasite. In this sense, we set out a mathematical model with... more
In this paper we analyse the Babesiosis transmission dynamics on bovines and ticks populations. Ticks play a role of infectious agents and vector of the protozoan Babesia hemo-parasite. In this sense, we set out a mathematical model with constant size population for the evolution of the infected bovines with Babesiosis and analyse its qualitative dynamics. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model varying the parameters show
di®erent scenarios about the spread of the disease
Key words: Babesiosis disease, Nonlinear dynamical systems, Global stability, Lyapunov methods, Simulations.
di®erent scenarios about the spread of the disease
Key words: Babesiosis disease, Nonlinear dynamical systems, Global stability, Lyapunov methods, Simulations.
Research Interests:
The 2009 swine flu pandemic was a global outbreak of a new strain of H1N1 influenza virus and there are more than 14,000 confirmed deaths worldwide. The aim of this paper is to propose new mathematical models to study different dynamics... more
The 2009 swine flu pandemic was a global outbreak of a new strain of H1N1 influenza virus and there are more than 14,000 confirmed deaths worldwide. The aim of this paper is to propose new mathematical models to study different dynamics of H1N1
influenza virus spread in selected regions around the world. Spatial and temporal elements are included in these models to reproduce the dynamics of AH1N1/09 virus. Different models are used since H1N1 influenza virus spread in regions with different contact structures are not the same. We rely on time series notifications of individuals to estimate some of the parameters of the models. We find that, in order to reproduce the time series data and the spread of the disease, it is convenient to suggest spatio-temporal models. Regions with only one wave are modelled with the classical SEIR model and regions with multiple waves using models with spatiotemporal elements.
Key words: AH1N1/09 influenza, Human population, Spatio- temporal, Mathematical epidemic model.
influenza virus spread in selected regions around the world. Spatial and temporal elements are included in these models to reproduce the dynamics of AH1N1/09 virus. Different models are used since H1N1 influenza virus spread in regions with different contact structures are not the same. We rely on time series notifications of individuals to estimate some of the parameters of the models. We find that, in order to reproduce the time series data and the spread of the disease, it is convenient to suggest spatio-temporal models. Regions with only one wave are modelled with the classical SEIR model and regions with multiple waves using models with spatiotemporal elements.
Key words: AH1N1/09 influenza, Human population, Spatio- temporal, Mathematical epidemic model.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Diego F. Aranda, Deccy Y. Trejos, José C. Valverde Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features... more
Diego F. Aranda, Deccy Y. Trejos, José C. Valverde
Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features such as; very short epidemiological cycles, serious forms of the disease, simultaneous circulation of the different serotypes of virus, infection by Aedes aegypti, which is currently greater than 90% in all national Territory located below 2200 masl, and urbanization within endemic zones as a result of violence in the country, which puts at risk approximately 25 million people living in this susceptible zones to disease transmission.
This approach presents an analysis of the quantitative dynamic of SEIR (Susceptible, Exposed, Infectious and Removed) mathematical model, describing the disease transmission among humans and vector population (Aedes aegypti) with control strategies for vector. The stability of the equilibrium point shows that the density of the vector must be kept near to zero throughout all year to avoid the coexistence of the host and the vector. Varying the most relevant parameters of the model simulates different hypothetical scenarios of infection on different types of population (humans and vector) and this allows the validation of the mathematical model.
Keywords: Dengue Disease, Vector population, Ecology, Global stability.
Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features such as; very short epidemiological cycles, serious forms of the disease, simultaneous circulation of the different serotypes of virus, infection by Aedes aegypti, which is currently greater than 90% in all national Territory located below 2200 masl, and urbanization within endemic zones as a result of violence in the country, which puts at risk approximately 25 million people living in this susceptible zones to disease transmission.
This approach presents an analysis of the quantitative dynamic of SEIR (Susceptible, Exposed, Infectious and Removed) mathematical model, describing the disease transmission among humans and vector population (Aedes aegypti) with control strategies for vector. The stability of the equilibrium point shows that the density of the vector must be kept near to zero throughout all year to avoid the coexistence of the host and the vector. Varying the most relevant parameters of the model simulates different hypothetical scenarios of infection on different types of population (humans and vector) and this allows the validation of the mathematical model.
Keywords: Dengue Disease, Vector population, Ecology, Global stability.
La toxoplasmosis puede generar efectos irreversibles en el desarrollo del feto. Este hecho y las posibilidades tecnológicas para su identificación y manejo temprano, la hacen de especial interés para los servicios de salud pública. El... more
La toxoplasmosis puede generar efectos irreversibles en el desarrollo del feto. Este hecho y las posibilidades tecnológicas para su identificación y manejo temprano, la hacen de especial interés para los servicios de salud pública. El distrito capital de Colombia, en el contexto de un estudio multicéntrico nacional, pretendió establecer la magnitud del evento determinando la prevalencia en recién nacidos de cuatro instituciones representativas de la ciudad. Materiales y métodos. Entre marzo y diciembre de 2009, se recolectaron 5.035 muestras de sangre de cordón umbilical, a las cuales se les practicó la prueba presuntiva para detección de IgM anti-Toxoplasma por el método ELISA y, en una submuestra de 395 niños, se midió la IgA anti-Toxoplasma por el método de referencia ISAGA. Resultados. Se encontraron 29 muestras positivas para IgM (0,57%) y 36 dudosas (0,71%): para IgA, se encontraron cuatro muestras positivas (1%). El seguimiento clínico y de laboratorio permitió confirmar dos casos, uno de ellos con coriorretinitis y calcificaciones cerebrales, y otro que presentó esplenomegalia. Se establece, al momento, una prevalencia de toxoplasmosis congénita, al menos, de 1 por cada 2.517 nacimientos. Conclusiones. Los resultados demuestran la presencia de la toxoplasmosis congénita en la ciudad y la necesidad de incluirla en los programas de tamización de los recién nacidos y de vigilancia de las enfermedades congénitas en el distrito capital de Colombia.
The prevalence of Babesiosis has increased in northern Antioquia (Colombia). Despite \-con\-ge\-ni\-tal\ Babesiosis is not a disease of epidemic proportions, an important amount of bovines die or have serious effects on the milk and meat... more
The prevalence of Babesiosis has increased in northern Antioquia (Colombia). Despite \-con\-ge\-ni\-tal\ Babesiosis is not a disease of epidemic proportions, an important amount of bovines die or have serious effects on the milk and meat production. Discussion of the basic concepts of the Babesiosis transmission dynamics on bovines and ticks populations are presented. The ticks in this model play a role of infectious agents and vector of the protozoan Babesia hemo-parasite. In this paper we present an initial model with constant size population for the evolution of the infected bovines with Babesiosis. We explore the dynamics of the Babesiosis disease at the population level using an epidemiological model. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model varying the parameters show different scenarios about the spread of the disease.
The prevalence of Toxoplasmosis has increased dramatically around the world. Despite congenital Toxoplasmosis being not a disease of epidemic proportions, a large number of humans die or have serious effects on the developing fetus. In... more
The prevalence of Toxoplasmosis has increased dramatically around the world. Despite congenital Toxoplasmosis being not a
disease of epidemic proportions, a large number of humans die or have serious effects on the developing fetus. In this paper we present an initial model with varying size population for the evolution of the infected people with Toxoplasmosis. We explore the dynamics of the Toxoplasmosis disease at the population level using an epidemiological model. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model done by varying parameters show different scenarios about the spread of the disease.
@ 2008 Elsevier Ltd. All rights reserved.
Keywords: Toxoplasmosis disease; Epidemiological model; Numerical solution; Simulation
disease of epidemic proportions, a large number of humans die or have serious effects on the developing fetus. In this paper we present an initial model with varying size population for the evolution of the infected people with Toxoplasmosis. We explore the dynamics of the Toxoplasmosis disease at the population level using an epidemiological model. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model done by varying parameters show different scenarios about the spread of the disease.
@ 2008 Elsevier Ltd. All rights reserved.
Keywords: Toxoplasmosis disease; Epidemiological model; Numerical solution; Simulation
The prevalence of Babesiosis has increased in northern Antioquia (Colombia). Despite congenital Babesiosis is not a disease of epidemic proportions, an important amount of bovines die or have serious e ects on the milk and meat... more
The prevalence of Babesiosis has increased in northern Antioquia (Colombia). Despite congenital Babesiosis is not a disease of epidemic proportions, an important amount of bovines die or have serious e ects on the milk and meat production. Discussion of the basic concepts of the Babesiosis transmission dynamics on bovines and ticks populations are presented. The ticks in this model play a role of infectious agents and vector of the protozoan Babesia hemo-parasite. In this paper we present an initial model with constant size population for the evolution of the infected bovines with Babesiosis. We explore the dynamics of the Babesiosis diseaseat the population level using an epidemiological model. Statistical data are used to estimate some of the parameters of the model. Numerical simulations of the model varying the parameters show di erent scenarios about the spread of the disease Key words: Babesiosis disease, Bovines and ticks population, Epidemic model,
Numerical solution, Simulation, Ecology
Numerical solution, Simulation, Ecology
Diego F. Aranda, Deccy Y. Trejos, José C. Valverde Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features... more
Diego F. Aranda, Deccy Y. Trejos, José C. Valverde
Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features such as; very short epidemiological cycles, serious forms of the disease, simultaneous circulation of the different serotypes of virus, infection by Aedes aegypti, which is currently greater than 90% in all national Territory located below 2200 masl, and urbanization within endemic zones as a result of violence in the country, which puts at risk approximately 25 million people living in this susceptible zones to disease transmission.
This approach presents an analysis of the quantitative dynamic of SEIR (Susceptible, Exposed, Infectious and Removed) mathematical model, describing the disease transmission among humans and vector population (Aedes aegypti) with control strategies for vector. The stability of the equilibrium point shows that the density of the vector must be kept near to zero throughout all year to avoid the coexistence of the host and the vector. Varying the most relevant parameters of the model simulates different hypothetical scenarios of infection on different types of population (humans and vector) and this allows the validation of the mathematical model.
Keywords: Dengue Disease, Vector population, Ecology, Global stability.
Dengue is a priority in regards of Colombia’s Public Health due to many factors, among which there is the re-emergence and viral transmission that represent growing behaviour features such as; very short epidemiological cycles, serious forms of the disease, simultaneous circulation of the different serotypes of virus, infection by Aedes aegypti, which is currently greater than 90% in all national Territory located below 2200 masl, and urbanization within endemic zones as a result of violence in the country, which puts at risk approximately 25 million people living in this susceptible zones to disease transmission.
This approach presents an analysis of the quantitative dynamic of SEIR (Susceptible, Exposed, Infectious and Removed) mathematical model, describing the disease transmission among humans and vector population (Aedes aegypti) with control strategies for vector. The stability of the equilibrium point shows that the density of the vector must be kept near to zero throughout all year to avoid the coexistence of the host and the vector. Varying the most relevant parameters of the model simulates different hypothetical scenarios of infection on different types of population (humans and vector) and this allows the validation of the mathematical model.
Keywords: Dengue Disease, Vector population, Ecology, Global stability.