The effectiveness of vaccine in the outbreak of diphtheria: mathematical model and simulation

Ilahi, Fadilah; Widiana, Ana

doi:10.1088/1757-899x/434/1/012006

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…Fungsi objektif yang dibangun dalam masalah kendali optimal ini, bertujuan untuk meminimalkan jumlah populasi terinfeksi. Secara matematis, hal ini dinyatakan sebagai persamaan (6).…”

Section: Masalah Kendali Optimalunclassified

Kendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar

Izzati¹,

Andriani²

2021

JIMT

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Indonesia is one of the countries where has not been free from diphtheria outbreak. During 2017-2019, there were 2870 diphtheria cases with 96 deaths. With the mortality rate 5-20%, makes studies regarding diphtheria prevention and management strategies become important to do. In this study, a SEIQR mathematical model was constructed by considering the factor of natural immunity rate in exposed individuals. Then, by considering the complete basic immunization coverage and the proportion of the number of individuals with natural immunity rate as control variables, the optimal control problem is formulated to minimize the number of infected poopulation. Optimal control using DOTcvpSB toolbox obtained that the number of exposed population in the model decreased from 4.9% to 0.75%, and the number of infected population decreased from 3.1% to 0.32%.

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“…Fungsi objektif yang dibangun dalam masalah kendali optimal ini, bertujuan untuk meminimalkan jumlah populasi terinfeksi. Secara matematis, hal ini dinyatakan sebagai persamaan (6).…”

Section: Masalah Kendali Optimalunclassified

Kendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar

Izzati¹,

Andriani²

2021

JIMT

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“…Torrea et al [ 28 ] have studied the diphtheria outbreak with the SIRM model. Ilahi and Widiana [ 29 ] have developed an SEIR model for the diphtheria outbreak and analyze vaccination's effectiveness against the outbreak. Matsuyama et al [ 30 ] have analyzed the sensitivity and ambiguity based on the basic reproductive ratio ℛ 0 of the diphtheria epidemic in the Rohingya refugee camp in Bangladesh.…”

Section: Introductionmentioning

confidence: 99%

Global Stability Analysis and Parameter Estimation for a Diphtheria Model: A Case Study of an Epidemic in Rohingya Refugee Camp in Bangladesh

Islam

Ahmed

Rahman

et al. 2022

Computational and Mathematical Methods in Medicine

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In this article, we have developed a deterministic Susceptible-Latent-Infectious-Recovered (SLIR) model for diphtheria outbreaks. Here, we have studied a case of the diphtheria outbreak in the Rohingya refugee camp in Bangladesh to trace the disease dynamics and find out the peak value of the infection. Both analytical and numerical investigations have been performed on the model to find several remarkable behaviors like the positive and bounded solution, basic reproductive ratio, and equilibria such as disease extinction equilibrium and disease persistence equilibrium which are characterized depending on the basic reproductive ratio and global stability of the model using Lyapunov function for both equilibria. Parameter estimation has been performed to determine the values of the parameter from the daily case data using numerical technique and determined the value of the basic reproductive number for the outbreak as R 0 = 5.86 .

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A Cost‐Effective Epidemiological Exposition of Diphtheria Outbreak by the Optimal Control Model: A Case Study of Rohingya Refugee Camp in Bangladesh

Islam,

Kabir,

Rahman

et al. 2024

Complexity

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We consider a deterministic optimal control approach with cost‐effectiveness analysis for the diphtheria outbreak in the Rohingya refugee camp in Bangladesh. A deterministic epidemic dynamical model for diphtheria outbreaks has been developed with three optimal controls: vaccination, latent, and infectious treatment. Here, the qualitative study of the model has been interpreted. An objective function has been regarded as a cost function introduced by the optimal controls and the diseases themselves. Then, the existence and uniqueness of the optimal system have also been shown with the help of Pontryagin’s minimum principle. A numerical investigation has been carried out to solve the state and adjoint systems of optimality conditions. Furthermore, it has been investigated using several levels of availability of the optimal controls (vaccination, latent, and infectious treatment) to identify which level gives the best outcomes. Moreover, the cost‐effective analysis has been inquired with the numerical value of the cost function and the total cured population in each control strategy to clarify the strategy with the least cost but maximum remediation.

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The effectiveness of vaccine in the outbreak of diphtheria: mathematical model and simulation

Cited by 3 publications

References 14 publications

Kendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar

Kendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar

Global Stability Analysis and Parameter Estimation for a Diphtheria Model: A Case Study of an Epidemic in Rohingya Refugee Camp in Bangladesh

A Cost‐Effective Epidemiological Exposition of Diphtheria Outbreak by the Optimal Control Model: A Case Study of Rohingya Refugee Camp in Bangladesh

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