In this paper we present a non-linear mathematical model which analyzes the spread of smoking in ... more In this paper we present a non-linear mathematical model which analyzes the spread of smoking in a population. The population is divided into five classes: potential smokers, occasional smokers, heavy smokers, temporary quitters and permanent quitters. We study the effect of considering the class of occasional smokers and the impact of adding this class to the smoking model in [1] on the stability of its equilibria. This model is similar to the model in [2] where we studied the effect of occasional smokers on potential smokers, but here we're going to consider the effect of heavy smokers on potential smokers and it's impact on the stability of the model. Numerical results are also given to support our results and to compair the two models.
In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide t... more In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide the population into four subclasses, one of them is the susceptible population S and the others are HIV infectives (HIV positives that do not know they are infected) I 1 , HIV positives that know they are infected (by way of medical screening or other ways) I 2 and that of AIDS patients A. Both the disease-free equilibrium and the infected endemic equilibrium are found and their stability is investigated using stability theory of delay differential equations. The effect of delay on the stability of the endemically infected equilibrium is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation when using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.
Almost all mathematical models of infectious diseases depend on subdividing the population into a... more Almost all mathematical models of infectious diseases depend on subdividing the population into a set of distinctive classes dependent upon experience with respect to the relevant disease. In our work we will classify individuals as either a susceptible individual S or an infected individual I. Two SIS epidemic models in two competing species are formulated and analyzed. The two species are both subject to a disease. We analyze two different types of incidence, standard incidence and mass action incidence. Thresholds are identified which determine the existence of equilibria, when the populations will survive and when the disease remains endemic. Also stability results are proved. Using Hopf bifurcation theory some results of complicated dynamic behavior of the models are shown. With the interinfection rate of disease between the two species as a bifurcation parameter, it is shown that the model exhibits a Hopf bifurcation leading to a family of periodic solutions. Mathematics Subje...
International journal of differential equations and applications, 2015
In this paper we present a non-linear mathematical model whichanalyzes the spread of smoking in a... more In this paper we present a non-linear mathematical model whichanalyzes the spread of smoking in a population. The population is dividedinto five classes: potential smokers, occasional smokers, heavy smokers,temporary quitters and permanent quitters. We study the effect ofconsidering the class of occasional smokers and the impact of adding thisclass to the smoking model in [1] on the stability of its equilibria.This model is similar to the model in [2], where we studied theeffect of occasional smokers on potential smokers, but here we're going toconsider the effect of heavy smokers on potential smokers and it's impact onthe stability of the model. Numerical results are also given to support ourresults and to compair the two models.
In this paper, we have proposed and analyzed a non-linear mathematical model of the issue of unem... more In this paper, we have proposed and analyzed a non-linear mathematical model of the issue of unemployment by considering three main variables, namely the numbers of unemployed, employed and available vacancies. The model resembles the situation in some countries where the support of the government reaches a certain limited level where the rate of creating new jobs becomes constant and can no longer be proportional to the number of unemployed due to limited financial and economics resources. The qualitative results for the mathematical model are obtained utilizing the stability theory of nonlinear differential equations. Furthermore, some numerical simulations are illustrated to support the qualitative results. Manuscript received 12th May 2020, revised 27th October 2020, accepted 1st December 2020.
One problem that has become a concern for governments around the world is unemployment. We illust... more One problem that has become a concern for governments around the world is unemployment. We illustrate the problem using a nonlinear system of differential equations considering three dynamical vari...
Almost all mathematical models of infectious diseases depend on subdividing the population into a... more Almost all mathematical models of infectious diseases depend on subdividing the population into a set of distinctive classes dependent upon experience with respect to the relevant disease. In our work we will classify individuals as either a susceptible individual S or an infected individual I. Two SIS epidemic models in two competing species are formulated and analyzed. The two species are both sub ject to a disease. We analyze two different types of incidence, standard incidence and mass action incidence. Thresholds are identified which determine the existence of equilibria, when the populations will survive and when the disease remains endemic. Also stability results are proved. Using Hopf bifurcation theory some results of complicated dynamic behavior of the models are shown. With the interinfection rate of disease between the two species as a bifurcation parameter, it is shown that the model exhibits a Hopf bifurcation leading to a family of periodic solutions
In this paper an SEIR epidemic model with a limited resource for treatment is investigated. It is... more In this paper an SEIR epidemic model with a limited resource for treatment is investigated. It is assumed that the treatment rate is proportional to the number of patients as long as this number is below a certain capacity and it becomes constant when that number of patients exceeds this capacity. Mathematical analysis is used to study the dynamic behavior of this model. Existence and stability of disease-free and endemic equilibria are investigated. It is shown that this kind of treatment rate leads to the existence of multiple endemic equilibria where the basic reproduction number plays a big role in determining their stability
In this paper we present a non-linear mathematical model which analyzes the spread of smoking in ... more In this paper we present a non-linear mathematical model which analyzes the spread of smoking in a population. The population is divided into five classes: potential smokers, occasional smokers, heavy smokers, temporary quitters and permanent quitters. We study the effect of considering the class of occasional smokers and the impact of adding this class to the smoking model in [1] on the stability of its equilibria. This model is similar to the model in [2] where we studied the effect of occasional smokers on potential smokers, but here we're going to consider the effect of heavy smokers on potential smokers and it's impact on the stability of the model. Numerical results are also given to support our results and to compair the two models.
In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide t... more In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide the population into four subclasses, one of them is the susceptible population S and the others are HIV infectives (HIV positives that do not know they are infected) I 1 , HIV positives that know they are infected (by way of medical screening or other ways) I 2 and that of AIDS patients A. Both the disease-free equilibrium and the infected endemic equilibrium are found and their stability is investigated using stability theory of delay differential equations. The effect of delay on the stability of the endemically infected equilibrium is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation when using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.
Almost all mathematical models of infectious diseases depend on subdividing the population into a... more Almost all mathematical models of infectious diseases depend on subdividing the population into a set of distinctive classes dependent upon experience with respect to the relevant disease. In our work we will classify individuals as either a susceptible individual S or an infected individual I. Two SIS epidemic models in two competing species are formulated and analyzed. The two species are both subject to a disease. We analyze two different types of incidence, standard incidence and mass action incidence. Thresholds are identified which determine the existence of equilibria, when the populations will survive and when the disease remains endemic. Also stability results are proved. Using Hopf bifurcation theory some results of complicated dynamic behavior of the models are shown. With the interinfection rate of disease between the two species as a bifurcation parameter, it is shown that the model exhibits a Hopf bifurcation leading to a family of periodic solutions. Mathematics Subje...
International journal of differential equations and applications, 2015
In this paper we present a non-linear mathematical model whichanalyzes the spread of smoking in a... more In this paper we present a non-linear mathematical model whichanalyzes the spread of smoking in a population. The population is dividedinto five classes: potential smokers, occasional smokers, heavy smokers,temporary quitters and permanent quitters. We study the effect ofconsidering the class of occasional smokers and the impact of adding thisclass to the smoking model in [1] on the stability of its equilibria.This model is similar to the model in [2], where we studied theeffect of occasional smokers on potential smokers, but here we're going toconsider the effect of heavy smokers on potential smokers and it's impact onthe stability of the model. Numerical results are also given to support ourresults and to compair the two models.
In this paper, we have proposed and analyzed a non-linear mathematical model of the issue of unem... more In this paper, we have proposed and analyzed a non-linear mathematical model of the issue of unemployment by considering three main variables, namely the numbers of unemployed, employed and available vacancies. The model resembles the situation in some countries where the support of the government reaches a certain limited level where the rate of creating new jobs becomes constant and can no longer be proportional to the number of unemployed due to limited financial and economics resources. The qualitative results for the mathematical model are obtained utilizing the stability theory of nonlinear differential equations. Furthermore, some numerical simulations are illustrated to support the qualitative results. Manuscript received 12th May 2020, revised 27th October 2020, accepted 1st December 2020.
One problem that has become a concern for governments around the world is unemployment. We illust... more One problem that has become a concern for governments around the world is unemployment. We illustrate the problem using a nonlinear system of differential equations considering three dynamical vari...
Almost all mathematical models of infectious diseases depend on subdividing the population into a... more Almost all mathematical models of infectious diseases depend on subdividing the population into a set of distinctive classes dependent upon experience with respect to the relevant disease. In our work we will classify individuals as either a susceptible individual S or an infected individual I. Two SIS epidemic models in two competing species are formulated and analyzed. The two species are both sub ject to a disease. We analyze two different types of incidence, standard incidence and mass action incidence. Thresholds are identified which determine the existence of equilibria, when the populations will survive and when the disease remains endemic. Also stability results are proved. Using Hopf bifurcation theory some results of complicated dynamic behavior of the models are shown. With the interinfection rate of disease between the two species as a bifurcation parameter, it is shown that the model exhibits a Hopf bifurcation leading to a family of periodic solutions
In this paper an SEIR epidemic model with a limited resource for treatment is investigated. It is... more In this paper an SEIR epidemic model with a limited resource for treatment is investigated. It is assumed that the treatment rate is proportional to the number of patients as long as this number is below a certain capacity and it becomes constant when that number of patients exceeds this capacity. Mathematical analysis is used to study the dynamic behavior of this model. Existence and stability of disease-free and endemic equilibria are investigated. It is shown that this kind of treatment rate leads to the existence of multiple endemic equilibria where the basic reproduction number plays a big role in determining their stability
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