Stability analysis of SEISEIR-SEI modelling on the dynamics of spread dengue fever with vaccination and insecticide

H, Hartati; Toaha, Syamsuddin; Kasbawati,

doi:10.1088/1742-6596/1341/6/062033

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…In epidemiology, the rate of spread of an infectious disease is usually measured by a value called the basic reproduction number ( ) ( [4,8,13]). .…”

Section: Basic Reproduction Numbersmentioning

confidence: 99%

Stability Analysis of Divorce Dynamics Models

Muaraf¹,

Toaha

Kasbawati

2020

JMSK

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This article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues methods. In addition, the basic reproduction number is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results.

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“…In epidemiology, the rate of spread of an infectious disease is usually measured by a value called the basic reproduction number ( ) ( [4,8,13]). .…”

Section: Basic Reproduction Numbersmentioning

confidence: 99%

Stability Analysis of Divorce Dynamics Models

Muaraf¹,

Toaha

Kasbawati

2020

JMSK

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“…Contohnya adalah penyebaran penyakit TBC, Demam Berdarah (DBD) atau HIV-AIDS dan lainlain. [3][4][5][6][7][12][13]. Model matematika mengenai penyebaran COVID-19 juga telah banyak diteliti oleh banyak peneliti yang mengkaji tentang dinamika penyebaran penyakit tersebut dalam populasi [2,[8][9][10][11]14].…”

Section: Pendahuluanunclassified

Mathematical Model of COVID-19 with Quarantine and Vaccination

HUkmah¹,

Nisardi²,

Sulma³

et al. 2023

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We present a mathematical model of COVID-19 disease by modifying the SEIR model. The model considers two additional compartments, quarantine (Q) and vaccination (V) which aim to control the spread of COVID-19. Based on the model, we obtained a disease-free equilibrium point and an endemic equilibrium point. The basic reproduction numbers were calculated using the next-generation matrix method. In this model, we analyzed the stability conditions that must be satisfied by the defining parameters. We perform data on the spread of COVID-19 in Indonesia for estimation to provide the parameter value in the model. Based on the result, there is an influence of changes in several parameter values on the number of individuals infected with COVID-19.

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“…Dinamika perubahan populasi merupakan salah satu kajian dalam pemodelan matematika yang mencoba mendeskripsikan fenomena dari sudut pandang matematika. Fenomena ditransformasikan ke dalam persamaan atau sistem persamaan, misalnya dalam populasi dinamis [3,4,5] dan di bidang epidemiologi [6,7,8]. Dengan asumsi bahwa penyalahgunaan narkoba dapat menyebar dari satu sama lain, dinamika penyebaran penyalahgunaan narkoba juga dapat dipertimbangkan dalam pemodelan matematis.…”

Section: Pendahuluanunclassified

Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

Anggriani

Toaha²,

Kasbawati³

2021

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This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

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Stability analysis of SEISEIR-SEI modelling on the dynamics of spread dengue fever with vaccination and insecticide

Cited by 8 publications

References 14 publications

Stability Analysis of Divorce Dynamics Models

Stability Analysis of Divorce Dynamics Models

Mathematical Model of COVID-19 with Quarantine and Vaccination

Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

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