Analisis Dinamik Model Penyebaran COVID-19 dengan Vaksinasi

Resmawan, Resmawan; Yahya, Lailany; Pakaya, Revandi S.; Panigoro, Hasan S.; Nuha, Agusyarif Rezka

doi:10.34312/jjbm.v3i1.13176

Cited by 5 publications

(5 citation statements)

References 10 publications

(11 reference statements)

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“…A key parameter of the system is the basic reproductive number of the disease in the predator, R 0 [28,29], defined by:…”

Section: Basic Reproductive Numbermentioning

confidence: 99%

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

Beay,

Leleury,

Rijoly

et al. 2023

Jambura J. Biomath.

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The growth dynamics of various species are affected by various aspects. Harvesting interventions and the spread of disease in species are two important aspects that affect population dynamics and it can be studied. In this work, we consider a stage-structure Leslie–Gower model with linear harvesting on the both prey and predator. Additionally, we also consider the infection aspect in the predator population. The population is divided into four subpopulations: immature prey, mature prey, susceptible predator, and infected predator. We analyze the existences and stabilities of feasible equilibrium points. Our results shown that the harvesting in prey and the disease in predator impacts the behavioral of system. The situation in the system is more complex due to disease in the predator population. Some numerical simulations are given to confirm our results.

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“…A key parameter of the system is the basic reproductive number of the disease in the predator, R 0 [28,29], defined by:…”

Section: Basic Reproductive Numbermentioning

confidence: 99%

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

Beay,

Leleury,

Rijoly

et al. 2023

Jambura J. Biomath.

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“…Sementara itu, Mu'tamar, et al [10] membahas model SIR dan pemberian vaksinasi dengan menggunakan kontrol optimum untuk menganalisis penyebaran COVID-19. Pola penyebaran COVID-19 dengan pendekatan model stokastik juga telah dilakukan dengan mempertimbangkan intervensi vaksinasi [11,12].…”

Section: Pendahuluanunclassified

“…berdasarkan persamaan(11) dan(12) diperoleh e * 1 + e * 2 < 0 serta e * 1 e * 2 > 0. Kondisi ini ekuivalen dengan e * 1 < 0 dan e * 2 < 0 yang menunjukkan bahwa tidak ada titik tetap kesetimbangan T 2 yang bernilai positif.…”

unclassified

Dinamika dan Stabilitas Populasi pada Model Penyebaran COVID-19 dengan Vaksinasi dan Migrasi Penduduk

Resmawan,

Yahya,

Nuha

et al. 2023

Jambura J. Math

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This article discusses the mathematical model of the spread of COVID-19 by considering vaccination and population migration. The former model is analyzed by determining the equilibrium point, basic reproduction number, analyzing the stability of the equilibrium point, sensitivity analysis, and accompanied by numerical simulation. Analysis of the stability of disease-free and endemic equilibrium points using the Routh-Hurwitz Criteria and the Castillo-Chaves and Song theorems. The results of the analysis show that there are two equilibrium points, namely a disease-free equilibrium point (T1), which is locally asymptotically stable when R0 1, and an endemic equilibrium point (T2), which is locally asymptotically stable when R0 1. Furthermore, the sensitivity analysis showed that the most sensitive parameters to changes in the basic reproduction number were the emigration rate parameter (m2) and the infection probability parameter after contact between infected and susceptible individuals without vaccination (h). In addition, the numerical simulation results show that the sensitive parameter values, namely m2, h, zse, g, and # have a significant effect on the basic reproduction numbers. Suppressing the chance of infection in susceptible individuals and the rate of contact between susceptible and exposed individuals, as well as increasing the number of individuals who emigrate and who are vaccinated, can reduce the transmission of COVID-19.

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“…Populations that can cause infection are Exposed and Infected populations. Then the system can be rewritten as vector F and vector V , namely [11]:…”

Section: Basic Reproduction Number Rmentioning

confidence: 99%

Dynamic analysis of SEIR model for Covid-19 spread in Medan

Sihaloho¹,

Nasution²

2022

Jambura J. Biomath.

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In this study, a mathematical model was studied on the population of the spread of Covid-19 in Medan which the model use an epidemic mathematical model, SEIR (Susceptible, Exposed, Infected, and Recovered). Next, we determine the basic reproduction number R0 using the next generation matrix and the equilibrium point which is analyzed using the Routh Hurwitz criteria. The disease-free equilibrium point is said to be locally asymptotically stable if R01 and the endemic equilibrium point is said to be locally asymptotically stable if R01. Numerical simulation of the model was carried out using real data on the number of Covid-19 cases in Medan and with the help of Maple software. Through the data obtained, the value of R01 indicates that Covid-19 at the time of the study was still contagious to other individuals. Furthermore, based on the simulation formed from the SEIR model with the given initial and parameters, it was found that the greater the contact rate or the transmission rate, the more spread the disease would be and the smaller the cure rate, the more the disease would spread.

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Analisis Dinamik Model Penyebaran COVID-19 dengan Vaksinasi

Cited by 5 publications

References 10 publications

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator

Dinamika dan Stabilitas Populasi pada Model Penyebaran COVID-19 dengan Vaksinasi dan Migrasi Penduduk

Dynamic analysis of SEIR model for Covid-19 spread in Medan

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