The objective of this paper is to study the reduction of an epidemiological simple SI given originally in partial differential equations into a model in delay differential equations. Originally, the population is divided in juvenile and adult groups. We assume that only the adult population is sexually active and that it is possible that infected adults may produce susceptible newborns and infected newborns. The global stability of the SI model in Delay Equations is studied in López-Cruz [5]

La dinámica del desarrollo celular en el timo es afectada por las interacciones de las diferentes subpoblaciones celulares. Experimentos recientes sugieren que las células madres T, podrían afectar el crecimiento y diferenciación de los timocitos inmaduros. Aquí se presenta el análisis y el modelamiento matemático sostenido con simulaciones computacionales que muestran el proceso de regulación celular. Nuestros resultados sugieren que cuando proporcionamos externamente células del tipo CD4+ T, estas afectan positivamente a la célula simple y positiva CD4+CD8- (subpoblación timocita), incrementando la diferenciación de las células doble positivo y reduciendo la célula tipo CD4+CD8-.

We present the analysis of a mathematical model applied to Epidemiology. It explains the dynamics of transmission of the disease of the Acquired Immunodeficiency Syndrome (AIDS) among eterosexually active people using natural and non natural protection. We study the sensitivity of the model with respect to its local stability to the Infection-Free Equilibrium Point and Computational Simulations. This provides an understanding of the dynamic of the model to take decisions in the area of Public Health, taking into account the social and economical aspects.

In this work, we analyze the stability of two epidemiological models of obesity. The first model only admits social influence, that is, the environment in which individuals live, the second model adds control to reduce obesity and excess weight. The obesity-free equilibrium point is local and asymptotically stable if R0 < 1 where R0 is a basic replacement rate. For the model with control, its stability is shown and it is appreciated numerically that it accelerates the decrease of obese individuals.

The objective of this paper is to study the reduction of an epidemiological simple SI given originally in partial differential equations into a model in delay differential equations. Originally, the population is divided in juvenile and adult groups. We assume that only the adult population is sexually active and that it is possible that infected adults may produce susceptible newborns and infected newborns. The global stability of the SI model in Delay Equations is studied in López-Cruz [5]

La dinámica del desarrollo celular en el timo es afectada por las interacciones de las diferentes subpoblaciones celulares. Experimentos recientes sugieren que las células madres T, podrían afectar el crecimiento y diferenciación de los timocitos inmaduros. Aquí se presenta el análisis y el modelamiento matemático sostenido con simulaciones computacionales que muestran el proceso de regulación celular. Nuestros resultados sugieren que cuando proporcionamos externamente células del tipo CD4+ T, estas afectan positivamente a la célula simple y positiva CD4+CD8- (subpoblación timocita), incrementando la diferenciación de las células doble positivo y reduciendo la célula tipo CD4+CD8-.

We present the analysis of a mathematical model applied to Epidemiology. It explains the dynamics of transmission of the disease of the Acquired Immunodeficiency Syndrome (AIDS) among eterosexually active people using natural and non natural protection. We study the sensitivity of the model with respect to its local stability to the Infection-Free Equilibrium Point and Computational Simulations. This provides an understanding of the dynamic of the model to take decisions in the area of Public Health, taking into account the social and economical aspects.

rlopezc@ulima.edu.pe;ecambillom@unmsm.edu.pe

rlopezc@ulima.edu.pe

In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing negative feedback and a nonpharmaceutical intervention. The first model to be defined is the usceptible–Isolated–Infected–Recovered–Dead (SAIRD) epidemics model and then the S-A-I-R-D-Information Index (SAIRDM) model that corresponds to coupling the SAIRD model with the negative feedback. Controlling the information about nonpharmaceutical interventions is considered by the addition of a new variable that measures how the behavioral changes about isolation influence pandemics. An analytic expression of a replacement ratio that depends on the absence of the negative feedback is determined. The results obtained show that the global stability of the disease-free equilibrium is determined by the value of a certain threshold parameter called the basic reproductive number R and the loca...

In this work, we analyze the stability of two epidemiological models of obesity. The first model only admits social influence, that is, the environment in which individuals live, the second model adds control to reduce obesity and excess weight. The obesity-free equilibrium point is local and asymptotically stable if R0 < 1 where R0 is a basic replacement rate. For the model with control, its stability is shown and it is appreciated numerically that it accelerates the decrease of obese individuals.

In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied. Estabilidad de un modelo depredador-presa tipo Leslie Gower con un efecto Allee fuerte con retardo The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.

A basic mathematical model in epidemiology is the SIR (Susceptible–Infected–Removed) model, which is commonly used to characterize and study the dynamics of the spread of some infectious diseases. In humans, the time scale of a disease can be short and not necessarily fatal, but in some animals (for example, insects) this same short time scale can make the disease fatal if we take into account their life expectancy. In this work, we will see how a positive feedback effect (decrease of the susceptible population at small densities) in a SIR model can cause a qualitative characterization of the dynamics defined by the original SIR model. Finally, we will also show with numerical simulations how a delay in the feedback effect causes very interesting qualitative changes of the system with epidemiological significance.

In this work, a suitable change of variable is established that allows transforming a differential equation with non-constant delay into another differential equation with constant delay. The analysis of this change of variable leads to the Abel functional equation, whose study guarantees the existence and uniqueness of this change of variable; in addition, an iterative method for the construction of such solution is established.

In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.

In the present work, a Basic Model SI with Vital Dynamics Structured by Gender developed by the Ordinary Differential Equations (Transmission of contagion is instantaneous), and also developed in the DelayDifferential Equations (Transmission of contagion occurs after a certain period of time), where the Local and Asymptotic Stability Theorem is proposed The Free of Infection point for both models, respectively.

In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.

In the present work, a Basic Model SI with Vital Dynamics Structured by Gender developed by the Ordinary Differential Equations (Transmission of contagion is instantaneous), and also developed in the DelayDifferential Equations (Transmission of contagion occurs after a certain period of time), where the Local and Asymptotic Stability Theorem is proposed The Free of Infection point for both models, respectively.

We propose a modification of the SLIAR (Susceptible- Latent-Symptomatic Infected- Asymptomatic- Recovered) mathematical-epidemiological model with vital dynamics. This model includes a vaccination control strategy, and a treatment to reduce the symptoms, also the symptomatic infected population is divided into two states according to its severity. The qualitative analysis shows the local stability of the disease-free equilibrium point and the endemic point. Simulations and the statistical sensitivity analysis are developed using a set of parameters for COVID-19, and we found that the transmission, recruitment, finally, vaccination rates are potential targets to control an outbreak.

A mathematical model is proposed to study the dynamics of the spread of HIV/AIDS with treatment considering media coverage. The subpopulations involved in the study are; susceptible individuals, slow-latency infected individuals, fast-latency infected individuals, symptomatic individuals undergoing treatment, and finally individuals with AIDS. We consider a system of ordinary differential equations that let us to understand the dynamics of the spread of HIV/AIDS, taking into account two non-linear incidence rates that show the influence of media coverage as a disease control. We establish conditions for the stability of this model. The result enables us to evaluate the media coverage impact on the dynamics of the disease. Finally, we show a numerical simulation analysis of the model and a sensitivity analysis corresponding to the parameters.