SVIR Epidemic Model with Non Constant Population

Harianto, Joko; Suparwati, Titik

doi:10.18860/ca.v5i3.5511

Cited by 2 publications

(5 citation statements)

References 6 publications

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“…Interpretation of analysis results is similar to the discussion in [13], [14], [15], [16], [17], [18], [19] and [20] that the primary reproduction number plays an important role to know the dynamics of the spread of disease. However, every primary reproduction number obtained varies depending on the parameters of the model formed.…”

Section: Ifsupporting

confidence: 82%

“…The number of individuals susceptible to disease is denoted by S (Susceptible), the number of individuals who have undergone a vaccination process denoted by V (Vaccination), the number of infected individuals denoted by I (Infected), and the number of individuals recovering from the disease denoted by R (Recovered). Mathematical models about the SVIR epidemic are widely discussed in several scientific articles, including [6], [7], [8][9], [10], [7], [11], [12], [13], [14], [15], [16], [17], [18], [19]and [20]. Models discussed in the article [6], [7], [8][9], [10], [7], [11], [12] and [13] is a continuous model of SIR epidemic with the addition of vaccination compartment.…”

Section: Introductionmentioning

confidence: 99%

“…In the same year, Hidayati discussed the model of SVIR [13] with the addition of an event factor saturated in the population. The SVIR model [13] focuses on a constant number of populations until 2018; Harianto added an unconstant assumption of the model's population and discussed it in the article [18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of Population Density on the Model of the Spread of Measles

Harianto

Tuturop

Angelika

2020

Numerical: J.Mat and Pend.Mat

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This study is expected to contribute to the health sector, specifically to describe the dynamics of the measles spread through the models that have been analyzed. One of the factors that became the focus of this study was reviewing the influence of population density on measles spread. The initial step formulated the model and then determined the primary reproduction number and analyzed the stability of the model equilibrium point. The results of the analysis of this model show that there are two conditions for the value of which is a requirement that the existence of two model equilibrium points as well as local stability is needed, namely and . When , there exists a unique equilibrium point, called the non-endemic equilibrium point denoted by . Conversely, when , there are two equilibrium points, namely and the endemic equilibrium point characterized by . The results of local stability analysis show that when , the equilibrium point is stable asymptotic locally. It means that if hold, then in a long time there will not be a spread of disease in the susceptible and vaccinated sub-population, or in other words, the outbreak of the disease will stop. Conversely, when equilibrium point is stable asymptotic locally. It means that if , then measles disease is still in the environment for an infinite time with the condition of the proportions of each sub-population approach to , , and .

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Section: Ifsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

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Effect of Population Density on the Model of the Spread of Measles

Harianto

Tuturop

Angelika

2020

Numerical: J.Mat and Pend.Mat

Self Cite

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“…A year later, Harianto and Suparwati continued discussing the SVIR model by adding different death rate assumptions for each population in the SVIR model. Its numerical analysis and simulation discuss in the article [11]. In the paper [1] until [11], The population growth assumes to increase exponentially.…”

Section: Introductionmentioning

confidence: 99%

“…Its numerical analysis and simulation discuss in the article [11]. In the paper [1] until [11], The population growth assumes to increase exponentially. The models in these articles are more realistic if their population growth uses logistic growth.…”

Section: Introductionmentioning

confidence: 99%

Local Dynamics of an SVIR Epidemic Model with Logistic Growth

Harianto

Sari

2020

CAUCHY

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Discussion of local stability analysis of SVIR models in this article is included in the scope of applied mathematics. The purpose of this discussion was to provide results of local stability analysis that had not been discussed in some articles related to the SVIR model. The SVIR models discussed in this article involve logistics growth in the vaccinated compartment. The results obtained, i.e. if the basic reproduction number less than one and m is positive, then there is one equilibrium point i.e. E0 is locally asymptotically stable. In the field of epidemiology, this means that the disease will disappear from the population. However, if the basic reproduction number more than one and b1 more than b, then there are two equilibrium points i.e. disease-free equilibrium point denoted by E0 and the endemic equilibrium point denoted by E1*. In this case the endemic equilibrium point E1* is locally asymptotically stable. In the field of epidemiology, this means that the disease will remain in the population. The numerical simulation supports these results.

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SVIR Epidemic Model with Non Constant Population

Cited by 2 publications

References 6 publications

Effect of Population Density on the Model of the Spread of Measles

Effect of Population Density on the Model of the Spread of Measles

Local Dynamics of an SVIR Epidemic Model with Logistic Growth

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