Analysis and Simulation of SIRI Model for Dengue Fever Transmission

Side, Syafruddin; Pratama, Muh. Isbar; Badwi, Nasiah; Sanusi, Wahidah

doi:10.17485/ijst/2020/v13i03/147852

Cited by 4 publications

(3 citation statements)

References 7 publications

(9 reference statements)

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“…The basic reproductive number is the expected value of the number of vulnerable populations becoming infected during the time of infection. The basic reproductive number is the dominant eigenvalue of the matrix [11]- [12]. (7) with a new infection rate matrix and an individual displacement rate matrix evaluated at a fixed point.…”

Section: Basic Reproduction Numbersmentioning

confidence: 99%

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

Med¹,

Syaripuddin

Hamdani

et al. 2023

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The Covid19 case dated 11 November 2021 recorded that the human population died from Covid19 (143,595 people) with confirmed cases (4,249,323 cases) and active cases (9,537 cases). Based on these data, it can be concluded that COVID-19 is an acute and deadly disease. In addition to deaths, due to Covid-19, namely the increase in divorce cases, decreased income in the economy and tourism. In this study, the author made a mathematical modeling of Covid19 type as an effort to prevent the spread of Covid19. In the modeling there are human populations susceptible to Covid19 , human populations have been vaccinated , human populations have not been vaccinated , human populations are exposed , human populations are infected with Covid19 , and human populations recovered from Covid19 . The research objectives are 1) to build a mathematical model of Covid19, 2) to determine the fixed point and basic reproduction numbers, and 3) to analyze the stability of the fixed point. This type of research includes applied science research. The research procedure is 1) observing real phenomena, 2) searching literature, 3) determining variables, parameters, and assumptions in mathematical modeling, 4) building a mathematical model of Covid19, 5) analyzing the Covid19 mathematical model in the form of fixed points, basic reproduction numbers, and fixed point stability. The results of the analysis 1) the mathematical model type has a fixed point without disease and an endemic fixed point, 2) a fixed point without disease is stable for the condition , and the endemic fixed point is stable for the condition .

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Section: Basic Reproduction Numbersmentioning

confidence: 99%

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

Med¹,

Syaripuddin

Hamdani

et al. 2023

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show abstract

“…Fakta terkini menunjukkan bahwa pasien yang sembuh dari penyakit DBD masih berpeluang untuk terinfeksi kembali. Hal ini memotivasi para peneliti untuk memodifikasi model SIR Joko Harianto, Katarina Lodia Tuturop menjadi model SIRS [16]- [17]. Beberapa model matematika untuk masalah transmisi virus dengue telah diteliti dengan mempertimbangkan populasi manusia yang konstan dan vektor sebagai fungsi waktu [4].…”

Section: Pendahuluanunclassified

Stability Analysis of the SIR-SI Model for Dengue Fever Transmission with Saturated Birth Rate

Harianto,

Tuturop

2023

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The SIR-SI mathematical model for the problem of dengue virus spread which has been discussed in previous studies has not involved the saturated birth rate of mosquito. This discussion aims to construct and analyze the SIR-SI model which involves competition factors in mosquito population growth so that the model used to predict the number of dengue virus infections becomes more realistic. In addition, sensitivity analysis and numerical simulations of the models that have been constructed are also discussed. The method used is a literature study using theories derived from reputable articles. The results of this discussion show that the existence of an equilibrium point and its stability depends on the basic reproduction number. If the basic reproduction number is less than one, the number of cases of dengue fever infection will decrease. However, if the basic reproduction number is more than one, the number of cases of dengue infection will not decrease and even tend to be constant at a certain number. The average parameter of bites carried out by one mosquito in all humans () is the most dominant in increasing the spread of dengue disease in humans. On the other hand, mosquitoes' natural death rate parameter () is the most dominant in reducing the spread of dengue fever in humans. This information provides input and evaluation to decision-makers in solving the problem of the spread of dengue fever.

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“…Here we will explain boundedness [Khan & Talukder, 2021, Rudin, 1987, find out the equilibrium [Side et al 2019] and basic reproduction number [Side et al, 2019] regarding the constant value of control variables…”

Section: Boundedness Equilibrium Point (Corruption-free) and Basic Re...mentioning

confidence: 99%

Dynamic Optimization Applied to a Criminological Model for Reducing the Spread of Societal Corruption

2022

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Corruption is rapidly affecting any country’s economic, democratic, financial, social, and political stability. It has been a consistent social phenomenon that happens in all civilizations. Only in the last 20 years has this phenomenon been given serious attention. It has different forms and different impacts on the economy as well as society as a whole. Economic growth is slowed by corruption, which also has a detrimental effect on business operations, employment, and investment. Additionally, it has a detrimental effect on tax revenues as well as the effectiveness of various financial aid programs. So, it is necessary to reduce this global problem. For this reason, we propose a nonlinear deterministic model for the transmission dynamics of societal corruption in terms of optimal control problem, using two time-dependent controls namely the efforts aimed at preventing corruption through the use of social networks, media, and social organizations; including a strong and effective anti-corruption policy, and also the attempt to encourage the punishment of corrupt people to analyze the model. The goal of this study is to reduce the problem of corruption. The results show that our proposed model can help to alleviate this social issue. Our findings also reveal that by using both control strategies instead of just one we get a more effective result. Overall, this research suggests that the impact of corruption can be reduced by implementing anti-corruption media and advertising campaigns, as well as exposing corrupted people to jail and punishing them.

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Analysis and Simulation of SIRI Model for Dengue Fever Transmission

Cited by 4 publications

References 7 publications

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

Stability Analysis of the SIR-SI Model for Dengue Fever Transmission with Saturated Birth Rate

Dynamic Optimization Applied to a Criminological Model for Reducing the Spread of Societal Corruption

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