Dynamic behaviour for a nonautonomous heroin epidemic model with time delay

Samanta, G. P.

doi:10.1007/s12190-009-0349-z

Cited by 82 publications

(71 citation statements)

References 13 publications

(22 reference statements)

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“…To the best of our knowledge, the research works on the nonautonomous epidemic dynamical models are very few (Thieme, [38,39]; Herzong and Redheffer, [18]; Zhang and Teng, [43,44]; Samanta, [35]). In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDS epidemic model through vertical and horizontal transmissions of infections, having two stages of the period of infection according to the developing progress of infection before AIDS would be detected, i.e., the asymptomatic and the symptomatic stages, with varying total population size and distributed time delay to become infectious (through horizontal transmission) due to intracellular delay between initial infection of a cell by HIV and the release of new virions.…”

Section: Discussionmentioning

confidence: 99%

“…The nonautonomous epidemic models can be regarded as an extension of the periodic epidemic models. To the best of our knowledge, the research works on the nonautonomous epidemic dynamical models are very few (Thieme, [38,39]; Herzong and Redheffer, [18]; Zhang and Teng, [43,44]; Samanta, [35]). Therefore, the research on the nonautonomous epidemic dynamical models is also very important.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a Nonautonomous Hiv/Aids Epidemic Model With Distributed Time Delay

Samanta¹

2010

Mathematical Modelling and Analysis

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Abstract. In this paper, we have considered a nonautonomous stage-structured HIV/AIDS epidemic model through vertical and horizontal transmissions of infections, having two stages of the period of infection according to the developing progress of infection before AIDS defined would be detected, with varying total population size and distributed time delay to become infectious (through horizontal transmission) due to intracellular delay between initial infection of a cell by HIV and the release of new virions. The infected people in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected people. We have introduced some new threshold values R0 and R * and further obtained that the disease will be permanent when R0 > 1 and the disease will be going to extinct when R * < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of a Nonautonomous Hiv/Aids Epidemic Model With Distributed Time Delay

Samanta¹

2010

Mathematical Modelling and Analysis

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“…Kemudian di tahun 2000 dilakukan pemodelan hubungan antara perokok, bukan perokok, dan penderita kanker paru-paru [9]. Samanta [10] pada tahun 2011 memodelkan perilaku merokok sebagai sistem dinamik nonotonomus dengan waktu tunda. Analisis kestabilan global pada model tersebut dilakukan pula dengan menggunakan fungsi Lyapunov.…”

Section: Pendahuluanunclassified

“…[9] dan Samanta [10], pada tahun 2016 Sutantiati [11] memodelkan perilaku perokok aktif, perokok pasif, dan pengaruhnya terhadap penderita penyakit kanker paru-paru. Berdasarkan model tersebut subpopulasi rentan tumbuh secara eksponensial.…”

Section: Pendahuluanunclassified

The Effect of Smoking Behavior in the Human Population Growth of Lung Cancer Patients

Wardah

Trisilowati

Kusumawinahyu

2017

Nat-B

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ABSTRAKArtikel ini membahas pengaruh perilaku merokok baik perokok aktif maupun perokok pasif terhadap pertumbuhan populasi penderita kanker paru-paru melalui model matematika. Terdapat empat subpopulasi dalam model ini, yaitu subpopulasi rentan, subpopulasi perokok aktif, subpopulasi perokok pasif, dan subpopulasi penderita kanker paru-paru. Analisis dinamik model meliputi penentuan titik kesetimbangan, syarat eksistensi titik kesetimbangan, dan analisis kestabilan lokal titik kesetimbangan. Berdasarkan hasil analisis diperoleh tiga titik kesetimbangan, yaitu titik yang menyatakan bahwa keempat subpopulasi punah, titik yang menyatakan bahwa hanya subpopulasi rentan yang mampu bertahan hidup, dan titik yang menyatakan bahwa keempat subpopulasi mampu bertahan hidup. Titik kesetimbangan pertama selalu eksis, sedangkan titik kesetimbangan kedua dan ketiga eksis dengan syarat tertentu. Kestabilan titik kesetimbangan pertama dicapai ketika laju pertumbuhan intrinsik kurang dari laju kematian alami, titik kesetimbangan kedua dan ketiga stabil dengan syarat tertentu. Simulasi numerik disajikan untuk mengilustrasikan hasil analisis. Hasil simulasi menunjukkan solusi numerik sesuai dengan hasil analisis. Hasil penelitian ini juga menunjukkan bahwa laju perokok pasif memegang peranan penting dalam penyebaran penderita kanker paru-paru.Kata kunci: analisis dinamik, perokok aktif, perokok pasif, kanker paru-paru. ABSTRACTThis article discusses a model of lung cancer as the effect of smoking behavior on both active and passive smoker. There are four subpopulations in this model, namely susceptible subpopulation, active smoker subpopulation, passive smoker subpopulation, and subpopulation of lung cancer. Dynamical analysis is conducted to determine the equilibrium point, existence condition for equilibrium point, and analyze their stability. Based on analysis result, there are three equilibrium points. First equilibrium point shows that all subpopulations extinct. Second equilibrium point shows that only susceptible subpopulation can survive, and the last equilibrium point shows that all subpopulations can survive. First equilibrium point always exists while the others exist under certain condition. The stability of first equilibrium point can be reached when the intrinsic growth rate is less than the death rate. Whereas, the others equilibrium points will be stable under certain condition. Numerical simulation is performed to illustrate the analysis result. It is shown that numerical results are in accordance with analysis result. These numerical simulations also indicate that the rate of passive smoker plays important role in the growth rate of lung cancer.Keywords: dynamical analysis, active smokers, passive smokers, lung cancer. PENDAHULUANBerdasarkan data dari Globocan [1] menyatakan bahwa jumlah penderita kanker semakin meningkat dari tahun ke tahun. Selanjutnya, Globocan [1] menyebutkan bahwa diagnosa kanker yang paling umum di dunia adalah kanker paru-paru, yaitu 1,8 juta atau 13% dari keseluruhan kasus kanker. Bebera...

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“…More recently, the White and Comiskey model has been modified to develop a heroin epidemic model with distributed time delays [43,68]. In [43] the restriction where the total population is constant was deleted, a delay effect in those returning to untreated drug taking from a treatment programme was included, and finally a delay model was developed.…”

Section: Epidemiological Models Of Drug Abusementioning

confidence: 99%

Uncertainty quantification in dynamical models. An application to cocaine consumption in Spain.

Monzó¹

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The present Ph.D. Thesis considers epidemiological mathematical models based on ordinary differential equations and shows its application to understand the cocaine consumption epidemic in Spain. Three mathematical models are presented to predict the evolution of the epidemic in the near future in order to select the model that best reflects the data. By the results obtained for the selected model, if there are not changes in cocaine consumption policies or in the economic environment, the cocaine consumption will increase in Spain over the next few years. Furthermore, we use different techniques to estimate 95% confidence intervals and, consequently, quantify the uncertainty in the predictions. In addition, using several techniques, we conducted a model sensitivity analysis to determine which parameters are those that most influence the cocaine consumption in Spain. These analysis reveal that prevention actions on cocaine consumer population can be the most effective strategy to control this trend. ResumenLa presente Tesis considera modelos matemáticos epidemiológicos basados en ecuaciones diferenciales ordinarias y muestra su aplicación para entender la epidemia del consumo de cocaína en España. Se presentan tres modelos matemáticos para predecir la evolución de dicha epidemia en un futuro próximo, con el objetivo de seleccionar el modelo que mejor refleja los datos. Por los resultados obtenidos para el modelo seleccionado, si no hay cambios en las políticas de consumo de cocaína ni en elámbito económico, el consumo de cocaína aumentará en los próximos años. Además, utilizamos diferentes técnicas para estimar los intervalos de confianza al 95% y, de esta forma, cuantificar la incertidumbre en las predicciones. Finalmente, utilizando diferentes técnicas, hemos realizado un análisis de sensibilidad para determinar qué parámetros son los que más influyen en el consumo de cocaína. Estos análisis revelan que las acciones de prevención sobre la población de consumidores de cocaína pueden ser la estrategia más efectiva para controlar esta tendencia. ResumLa present Tesi considera models matemàtics epidemiològics basats en equacions diferencials ordinàries i mostra la seua aplicació per a entendre l'epidèmia del consum de cocaïna en Espanya. Es presenten tres models matemàtics per a predir l'evolució d'aquesta epidèmia en un futur pròxim, amb l'objectiu de seleccionar el model que millor reflecteix les dades. Pels resultats obtinguts per al model seleccionat, si no hi ha canvis en les polítiques de consum de cocaïna ni en l'àmbit econòmic, el consum de cocaïna augmentarà en els pròxims anys. A més, utilitzem diferents tècniques per a estimar els intervals de confiança al 95% i, d'aquesta manera, quantificar la incertesa en les prediccions. Finalment, utilitzant diferents tècniques, hem realitzat un anàlisi de sensibilitat per a determinar quins paràmetres són els que més influencien el consum de cocaïna. Aquestos anàlisis revelen que les accions de prevenció en la població de consumidors de cocaïna poden ser l'...

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Dynamic behaviour for a nonautonomous heroin epidemic model with time delay

Cited by 82 publications

References 13 publications

Analysis of a Nonautonomous Hiv/Aids Epidemic Model With Distributed Time Delay

Analysis of a Nonautonomous Hiv/Aids Epidemic Model With Distributed Time Delay

The Effect of Smoking Behavior in the Human Population Growth of Lung Cancer Patients

Uncertainty quantification in dynamical models. An application to cocaine consumption in Spain.

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