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Papers by Manuel Delgado Moya

Research paper thumbnail of A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis

BIOMATH

HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adher... more HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equil...

Research paper thumbnail of Mathematical Models for the Zika Epidemic

The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmi... more The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever) and Aedes albopictus. The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the ZIKV throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person's sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the ZIKV epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay, which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants and, to facilitate the work with the models, we provide a graphical user interface. Computational simulations are performed for Suriname and El Salvador, which are countries that are prone to develop the epidemic in an endemic manner. In order to study the spatial diffusion of ZIKV, we propose a model based on advection-diffusion equations and create a numerical scheme with finite elements and finite differences to resolve it.

Research paper thumbnail of Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in Suriname and El Salvador

Selecciones Matemáticas, 2019

Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in ... more Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in Suriname and El Salvador. Modelos Matemáticos para Zika con Variables Expuesto y retardo. Comparación y Experimentación en Surinam y El Salvador.

Research paper thumbnail of Modelo Estocástico Para La Epidemia Del Vih/Sida

Revista de Matemática: Teoría y Aplicaciones, 2017

La epidemia del VIH/SIDA le ha costado a la humanidad innumerables pérdidas tanto materiales como... more La epidemia del VIH/SIDA le ha costado a la humanidad innumerables pérdidas tanto materiales como humanas, su estudio se ha convertido en una prioridad para la comunidad científica mundial, con la idea de establecer una política efectiva de control y posteriormente de erradicación. Eneste trabajo se propone un modelo con Cadenas de Markov basado en el análisis de la matriz de transición con vista a diseñar una estrategia futura para reducir la aparición de nuevos casos y disminuir la letalidad de esta epidemia.

Research paper thumbnail of Estudio comparativo del consumo de aceite de oliva virgen o seje sobre el perfil lipídico y la resistencia a la oxidación de las lipoproteínas de alta densidad (HDL) del plasma de rata

Archivos latinoamericanos de nutrición

Research paper thumbnail of A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

Contemporary Mathematics, 2021

Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical ... more Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical model for the study of the effectiveness of therapy in TB to determine the impact of HIV/AIDS and diabetes in the spread of the disease and drug resistance. Our model takes into account the relationships between TB, HIV/AIDS, and diabetes and we also study the behavior of multidrug-resistance (MDR-TB) and extensively drug-resistant (XDR-TB). The main mathematical and epidemiology features of the model are investigated. The basic reproduction number (R0) in the different sub-populations (diabetics, HIV/AIDS, and those who do not suffer from these diseases) was studied. Conditions were obtained on the model parameters to know when the growth of the parameters associated with resistance to TB treatment has a negative impact on the transmission of TB in the population based on the R0 study. It is concluded that MDR-TB and XDR-TB have a negative impact on TB control. Computational simulations...

Research paper thumbnail of Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes

matemáticos para o estudo da aderência ao tratamento da tuberculose levando em conta os efeitos d... more matemáticos para o estudo da aderência ao tratamento da tuberculose levando em conta os efeitos do HIV/AIDS e diabetes. Tese (Doutorado).

Research paper thumbnail of Mathematical Model for the ZIKA Epidemic using Ordinary Equations and with Temporary Delay

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018

Zika virus is primarily transmitted to people through the bite of an infected mosquito from the A... more Zika virus is primarily transmitted to people through the bite of an infected mosquito from the Aedes genus, mainly Aedes aegypti in tropical regions. Aedes mosquitoes usually bite during the day, peaking during early morning and late afternoon/evening. This is the same mosquito that transmits dengue, chikungunya and yellow fever. Zika is transmitted to humans primarily through bites from infected Aedes aegypti and Aedes albopictus mosquitoes. The transmission is in both directions, that is, infected mosquitoes infect humans and infected humans infect mosquitoes. Sexual transmission of Zika virus is also possible. Other modes of transmission such as blood transfusion are being investigated. In this work are presented mathematical models to predict the behavior of the ZIKA epidemic over time, using ordinary differential equations [6, 14] and ordinary differential equations with temporal delay [11]. The delay is the time it takes humans and mosquitoes to develop the virus, become infected and participate in the transmission dynamics [9, 11]. The computer simulations are performed for Suriname and El Salvador, which have different characteristics, Suriname have higher rate the infection of human to mosquito and El Salvador have from mosquito to human, and this allows us to adapt the models to different epidemiological conditions. The data of the parameters and initial conditions were extracted from [5, 12, 13, 16].

Research paper thumbnail of Mathematical model of Diffusion-Advection for Zika

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018

Zika virus spreads to people primarily through the bite of an infected Aedes species mosquito (Ae... more Zika virus spreads to people primarily through the bite of an infected Aedes species mosquito (Ae. aegypti and Ae. albopictus). Zika can also be passed through sex from a person who has Zika to his or her sex partners and it can be spread from a pregnant woman to her fetus. People can protect themselves from mosquito bites and getting Zika through sex. ZIKV continues to spread geographically to areas where competent vectors are present. Although a decline in cases of Zika virus infection has been reported in some countries, or in some parts of countries, vigilance needs to remain high. In this work we propose a mathematical model that uses diffusion-advection equations to study the impact of the Zika epidemic. We present a numerical scheme linked to the finite elements method (FEM) with finite differences to solve the model. The computer simulations are performed for Suriname and El Salvador which have different characteristics and allow us to extend the study to other regions.

Research paper thumbnail of Mathematical model for the study of the diffusion of Zika. Computational experimentation in Paramaribo and Santa Ana

Selecciones Matemáticas, 2019

Mathematical model for the study of the diffusion of Zika. Computational experimentation in Param... more Mathematical model for the study of the diffusion of Zika. Computational experimentation in Paramaribo and Santa Ana. Modelo Matemático para el estudio de la difusión del Zika. Experimentación computacional en Paramaribo y Santa Ana.

Research paper thumbnail of Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes

Jambura Journal of Biomathematics (JJBM)

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatm... more In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in the Caputo sense. This model takes into account the relationship between Tuberculosis, HIV/AIDS, and diabetes and differentiates resistance cases into MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant tuberculosis). We present the basic results associated with the model and study the behavior of the disease-free equilibrium points in the different sub-populations, TB-Only, TB-HIV/AIDS, and TB-Diabetes. We performed computational simulations for different fractional orders (α-values) using an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among the results obtained, we have that the MDR-TB cases in all sub-populations decrease at the beginning of the study for the different α-values. In XDR-TB cases in the TB-Only sub-population, there is a decrease in the number of cases. XDR-TB cases in the TB-HIV/AIDS sub...

Research paper thumbnail of 2018- Vol32- num1- Estudio estocástico con el uso de cadenas de Markov para la transmisión del dengue

Revista Uniciencia, 2018

El dengue es una enfermedad viral transmitida a los seres humanos por picaduras del mosquito Aede... more El dengue es una enfermedad viral transmitida a los seres humanos por picaduras del mosquito Aedes aegypti, que puede conducir a diferentes estadios de la enfermedad. Esta enfermedad se ha extendido a gran parte del mundo y afecta a millones de personas. En este trabajo se presenta un estudio basado en la matriz de transición de una cadena de Markov homogénea, donde sus estados coinciden con las posibles etapas por las cuales una persona transita en la dinámica de transmisión del dengue y el comportamiento de las entidades que varían en el tiempo. También propone una estrategia novedosa de control basada en la ponderación de las probabilidades trascendentales incorporándolo a la matriz con el objetivo de reducir el impacto de la epidemia en la sociedad. La idea de ponderar determinadas probabilidades con estrategias de control brinda opciones para los sistemas de salud en el control de epidemias y el mejoramiento de las calidad de vida de los seres humanos, con una herramienta como las cadenas de Markov, cuyo éxito radica en que es suficientemente complejo para describir ciertas características no triviales de algunos sistemas, pero al mismo tiempo fácil de analizar matemáticamente.

Research paper thumbnail of A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis

BIOMATH

HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adher... more HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equil...

Research paper thumbnail of Mathematical Models for the Zika Epidemic

The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmi... more The Zika Virus (ZIKV) is a virus transmitted by Aedes aegypti mosquitoes (same as the one transmitting dengue and chikungunya fever) and Aedes albopictus. The main way of contagion by the ZIKV is caused by the bite of a mosquito that, after feeding from someone contaminated, can transport the ZIKV throughout its life, transmitting the disease to a population that does not have the immunity. It can also be transmitted through a person's sexual relationship with ZIKV to their partners, even if the infected person does not have the symptoms of the disease. In this work, we present two mathematical models for the ZIKV epidemic by using (1) ordinary differential equations and, (2) ordinary differential equations with temporal delay, which is the time it takes mosquitoes to develop the virus. We make a comparison between the two modeling variants and, to facilitate the work with the models, we provide a graphical user interface. Computational simulations are performed for Suriname and El Salvador, which are countries that are prone to develop the epidemic in an endemic manner. In order to study the spatial diffusion of ZIKV, we propose a model based on advection-diffusion equations and create a numerical scheme with finite elements and finite differences to resolve it.

Research paper thumbnail of Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in Suriname and El Salvador

Selecciones Matemáticas, 2019

Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in ... more Mathematical models for Zika with exposed variables and delay. Comparison and experimentation in Suriname and El Salvador. Modelos Matemáticos para Zika con Variables Expuesto y retardo. Comparación y Experimentación en Surinam y El Salvador.

Research paper thumbnail of Modelo Estocástico Para La Epidemia Del Vih/Sida

Revista de Matemática: Teoría y Aplicaciones, 2017

La epidemia del VIH/SIDA le ha costado a la humanidad innumerables pérdidas tanto materiales como... more La epidemia del VIH/SIDA le ha costado a la humanidad innumerables pérdidas tanto materiales como humanas, su estudio se ha convertido en una prioridad para la comunidad científica mundial, con la idea de establecer una política efectiva de control y posteriormente de erradicación. Eneste trabajo se propone un modelo con Cadenas de Markov basado en el análisis de la matriz de transición con vista a diseñar una estrategia futura para reducir la aparición de nuevos casos y disminuir la letalidad de esta epidemia.

Research paper thumbnail of Estudio comparativo del consumo de aceite de oliva virgen o seje sobre el perfil lipídico y la resistencia a la oxidación de las lipoproteínas de alta densidad (HDL) del plasma de rata

Archivos latinoamericanos de nutrición

Research paper thumbnail of A Mathematical Model for the Study of Effectiveness in Therapy in Tuberculosis Taking into Account Associated Diseases

Contemporary Mathematics, 2021

Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical ... more Tuberculosis (TB) remains a major global health problem. We present a deterministic mathematical model for the study of the effectiveness of therapy in TB to determine the impact of HIV/AIDS and diabetes in the spread of the disease and drug resistance. Our model takes into account the relationships between TB, HIV/AIDS, and diabetes and we also study the behavior of multidrug-resistance (MDR-TB) and extensively drug-resistant (XDR-TB). The main mathematical and epidemiology features of the model are investigated. The basic reproduction number (R0) in the different sub-populations (diabetics, HIV/AIDS, and those who do not suffer from these diseases) was studied. Conditions were obtained on the model parameters to know when the growth of the parameters associated with resistance to TB treatment has a negative impact on the transmission of TB in the population based on the R0 study. It is concluded that MDR-TB and XDR-TB have a negative impact on TB control. Computational simulations...

Research paper thumbnail of Mathematical models for the study of adherence to tuberculosis treatment taking into account the effects of HIV/AIDS and diabetes

matemáticos para o estudo da aderência ao tratamento da tuberculose levando em conta os efeitos d... more matemáticos para o estudo da aderência ao tratamento da tuberculose levando em conta os efeitos do HIV/AIDS e diabetes. Tese (Doutorado).

Research paper thumbnail of Mathematical Model for the ZIKA Epidemic using Ordinary Equations and with Temporary Delay

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018

Zika virus is primarily transmitted to people through the bite of an infected mosquito from the A... more Zika virus is primarily transmitted to people through the bite of an infected mosquito from the Aedes genus, mainly Aedes aegypti in tropical regions. Aedes mosquitoes usually bite during the day, peaking during early morning and late afternoon/evening. This is the same mosquito that transmits dengue, chikungunya and yellow fever. Zika is transmitted to humans primarily through bites from infected Aedes aegypti and Aedes albopictus mosquitoes. The transmission is in both directions, that is, infected mosquitoes infect humans and infected humans infect mosquitoes. Sexual transmission of Zika virus is also possible. Other modes of transmission such as blood transfusion are being investigated. In this work are presented mathematical models to predict the behavior of the ZIKA epidemic over time, using ordinary differential equations [6, 14] and ordinary differential equations with temporal delay [11]. The delay is the time it takes humans and mosquitoes to develop the virus, become infected and participate in the transmission dynamics [9, 11]. The computer simulations are performed for Suriname and El Salvador, which have different characteristics, Suriname have higher rate the infection of human to mosquito and El Salvador have from mosquito to human, and this allows us to adapt the models to different epidemiological conditions. The data of the parameters and initial conditions were extracted from [5, 12, 13, 16].

Research paper thumbnail of Mathematical model of Diffusion-Advection for Zika

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2018

Zika virus spreads to people primarily through the bite of an infected Aedes species mosquito (Ae... more Zika virus spreads to people primarily through the bite of an infected Aedes species mosquito (Ae. aegypti and Ae. albopictus). Zika can also be passed through sex from a person who has Zika to his or her sex partners and it can be spread from a pregnant woman to her fetus. People can protect themselves from mosquito bites and getting Zika through sex. ZIKV continues to spread geographically to areas where competent vectors are present. Although a decline in cases of Zika virus infection has been reported in some countries, or in some parts of countries, vigilance needs to remain high. In this work we propose a mathematical model that uses diffusion-advection equations to study the impact of the Zika epidemic. We present a numerical scheme linked to the finite elements method (FEM) with finite differences to solve the model. The computer simulations are performed for Suriname and El Salvador which have different characteristics and allow us to extend the study to other regions.

Research paper thumbnail of Mathematical model for the study of the diffusion of Zika. Computational experimentation in Paramaribo and Santa Ana

Selecciones Matemáticas, 2019

Mathematical model for the study of the diffusion of Zika. Computational experimentation in Param... more Mathematical model for the study of the diffusion of Zika. Computational experimentation in Paramaribo and Santa Ana. Modelo Matemático para el estudio de la difusión del Zika. Experimentación computacional en Paramaribo y Santa Ana.

Research paper thumbnail of Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes

Jambura Journal of Biomathematics (JJBM)

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatm... more In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in the Caputo sense. This model takes into account the relationship between Tuberculosis, HIV/AIDS, and diabetes and differentiates resistance cases into MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant tuberculosis). We present the basic results associated with the model and study the behavior of the disease-free equilibrium points in the different sub-populations, TB-Only, TB-HIV/AIDS, and TB-Diabetes. We performed computational simulations for different fractional orders (α-values) using an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among the results obtained, we have that the MDR-TB cases in all sub-populations decrease at the beginning of the study for the different α-values. In XDR-TB cases in the TB-Only sub-population, there is a decrease in the number of cases. XDR-TB cases in the TB-HIV/AIDS sub...

Research paper thumbnail of 2018- Vol32- num1- Estudio estocástico con el uso de cadenas de Markov para la transmisión del dengue

Revista Uniciencia, 2018

El dengue es una enfermedad viral transmitida a los seres humanos por picaduras del mosquito Aede... more El dengue es una enfermedad viral transmitida a los seres humanos por picaduras del mosquito Aedes aegypti, que puede conducir a diferentes estadios de la enfermedad. Esta enfermedad se ha extendido a gran parte del mundo y afecta a millones de personas. En este trabajo se presenta un estudio basado en la matriz de transición de una cadena de Markov homogénea, donde sus estados coinciden con las posibles etapas por las cuales una persona transita en la dinámica de transmisión del dengue y el comportamiento de las entidades que varían en el tiempo. También propone una estrategia novedosa de control basada en la ponderación de las probabilidades trascendentales incorporándolo a la matriz con el objetivo de reducir el impacto de la epidemia en la sociedad. La idea de ponderar determinadas probabilidades con estrategias de control brinda opciones para los sistemas de salud en el control de epidemias y el mejoramiento de las calidad de vida de los seres humanos, con una herramienta como las cadenas de Markov, cuyo éxito radica en que es suficientemente complejo para describir ciertas características no triviales de algunos sistemas, pero al mismo tiempo fácil de analizar matemáticamente.