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

Islam, Zahurul; Ahmed, Shohel; Rahman, Md. Mustafizur; Karim, M Abdel; Amin, Maryse

doi:10.1155/2022/6545179

Cited by 5 publications

(3 citation statements)

References 35 publications

(39 reference statements)

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“…Several previous studies modeling the problem of diphtheria spread include Islam et al [9] in 2022, the SLIR model was developed by assuming the latent population as asymptomatic diphtheria-infected individuals and this latent population cannot transmit diphtheria. In 2017, Sornbundit et al [10] developed a SIR epidemic model to determine the spread of diphtheria in 77 provinces of Thailand.…”

Section: Introductionmentioning

confidence: 99%

“…This study was developed from the SLIR model studied by Islam et al [9] namely dividing the infected population into infected with symptoms and infected without symptoms, dividing the recovered population into recovered with full immunity and recovered with partial immunity, and assuming the population recovered can be reinfected. The model in this study also maintains optimal control in the form of vaccinations for susceptible populations and treatment for infected populations.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control of Mathematical Model of Diphtheria Spreading

Amalia

Toaha²

2022

JDM

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This article examines optimal control model for the spread of diphtheria disease. Diphtheria is an infectious disease caused by the bacterium Corynebacterium diphtheriae. This model is divided into six compartments, namely population of susceptibles (𝑆), population of latent (L), population of infected with symptoms (Is), population of infected without symptoms (Ia), population of recovered with full immunity (Rf) and population of recovered with partial immunity (Rp). Two optimal controls are applied in the model, namely vaccination and treatment. The problem of optimal control is solved by using Pontryagin's minimal principle, which consists in solving a set of necessary conditions that must be satisfied by the optimal control and its associated state. The numerical method used to solve the optimal control problem is the forward-backward sweep method. Based on the results of numerical simulations, both controls should be administered in large numbers and continuously since the beginning of observation in order to reduce the number of diphtheria infected population and to control the spread of diphtheria.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Control of Mathematical Model of Diphtheria Spreading

Amalia

Toaha²

2022

JDM

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“…Izzati & Andriani (2021) discussed the SEIQR model by considering the rate of natural immunity of the exposed individuals in the spread of diphtheria. While other studies about the diphtheria disease model with the quarantine of exposed individuals analyzed the global stability and parameter estimation (Adewale, et al, 2017;Islam, Ahmed, Rahman, Karim, & Amin, 2022). Therefore, this study aims to construct and analyze the diphtheria spread model by considering transmission by contacting an exposed or infected individual, progression for vaccinated exposed individuals, quarantine for both exposed and infected people, and hand-washing behavior.…”

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confidence: 99%

Model Analysis of Diphtheria Disease Transmission with Vaccination, Quarantine, and Hand-Washing Behavior

Rahmi¹,

Pratama

2023

JTAM

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Recently, diphtheria outbreaks occur in many countries. According to the latest data from the World Health Organization, the number of registered cases and incidence of diphtheria in 2021 will be 8,638 cases worldwide. Diphtheria is generally an acute respiratory infection with most infections being asymptomatic or having a relatively slight clinical course. However, many sufferers are afflicted by breathing obstruction. In this study, we developed and analyzed the diphtheria spread model by considering transmission by contact with an exposed and infected individual, progression for vaccinated exposed individuals becoming infected, quarantine for both exposed and infected people, and hand-washing behavior. Besides that, we proved the stability analysis around the equilibrium points and did the numerical simulations of models. The results of this study show that the model system has two steady states, namely disease-free equilibrium and endemic equilibrium. The disease-free equilibrium is stable if the basic reproduction number is less than one, either is unstable. The endemic equilibrium exists and is stable if the basic reproduction number is greater than one. The numerical simulations show that there is a significant effect of vaccination, quarantine, and hand-washing behavior for infected numbers, respectively. Vaccination, quarantine, and hand-washing behavior could significantly reduce the basic reproductive and the infected number. Whereas vaccination for exposed people could increase the basic reproductive and the infected number.

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

Cited by 5 publications

References 35 publications

Optimal Control of Mathematical Model of Diphtheria Spreading

Optimal Control of Mathematical Model of Diphtheria Spreading

Model Analysis of Diphtheria Disease Transmission with Vaccination, Quarantine, and Hand-Washing Behavior

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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