Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach

Gu, Yu; Khan, Mohabat; Zarin, Rahat; Khan, Amir; Yusuf, Abdullahi; Humphries, Usa Wannasingha

doi:10.1016/j.aej.2022.10.057

Cited by 21 publications

(8 citation statements)

References 33 publications

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“…There are many different types of models that can be used, ranging from simple models that focus on a single aspect of the disease, to complex models that take into account multiple factors such as demographics, behavior, and interventions. In order to make accurate predictions, it is important to have accurate data on the disease in question, as well as a good understanding of the underlying biology and epidemiology [69] , [70] , [71] , [72] , [73] , [74] . However, even with the best data and models, there is always uncertainty in predictions about infectious diseases, as the dynamics of disease spread can be unpredictable and influenced by many factors.…”

Section: Mathematical Modelmentioning

confidence: 99%

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Chu¹,

Zarin²,

Khan³

et al. 2023

Alexandria Engineering Journal

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Section: Mathematical Modelmentioning

confidence: 99%

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Chu¹,

Zarin²,

Khan³

et al. 2023

Alexandria Engineering Journal

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“…Fractionalorder SEIR-type models and discrete-time epidemic models were used to characterise the dynamics of COVID-19 outbreaks (Paul et al, 2022;Khalaf et al, 2023;Li et al, 2023;). In addition, stability analyses of fractional-order epidemic models were performed for different virus transmissions such as Nipah and Dengue (Baleanu et al, 2023;Gu et al, 2023).…”

Section: Introductionmentioning

confidence: 99%

Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey

TAŞ,

KARA

2024

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The stability analysis of an epidemic model that takes into account the impact of vaccination and hospitalization is investigated in this study. Disease-free and endemic equilibrium points are obtained for the stability analysis. The necessary conditions for analyzing local stability at equilibrium points as well as global stability at the disease-free equilibrium point are also defined. Using data from three different periods corresponding to the emergence of three different variants of the COVID-19 outbreak in Turkey, the numerical simulation with graph fitting for the model is also taken into account. The analysis considers the efficacy of vaccination in restricting the virus's spread.

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“…The use of real incidence data is also needed to calibrate the performance of the model. There are many approaches that can be used to construct the dengue transmission model, such as with ordinary differential equations [24, 25], partial differential equations [26,27], fractional-order differential equations [28,29], stochastic differential equations [30][31][32], and other approaches.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of the impact of community ignorance on the population dynamics of dengue

Aldila

Puspadani

Rusin

2023

Front. Appl. Math. Stat.

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This study proposes a dengue spread model that considers the nonlinear transmission rate to address the level of human ignorance of dengue in their environment. The SIR − UV model has been proposed, where SIR denotes the classification of the human population and UV denotes the classification of the mosquito population. Assuming that the total human population is constant, and the mosquito population is already in its steady-state condition, using the Quasi-Steady State Approximation (QSSA) method, we reduce our SIR − UV model into a more simple IR-model. Our analytical result shows that a stable disease-free equilibrium exists when the basic reproduction number is <1. Furthermore, our model also shows the possibility of a backward bifurcation. The more ignorant the society is about dengue, the higher the possibility that backward bifurcation phenomena may appear. As a result, the condition of the basic reproduction number being <1 is insufficient to guarantee the extinction of dengue in a population. Furthermore, we found that increasing the recovery rate, reducing the waning immunity rate, and mosquito life expectancy can reduce the possibility of backward bifurcation phenomena. We use dengue incidence data from Jakarta to calibrate the parameters in our model. Through the fast Fourier transform analysis, it was found that dengue incidence in Jakarta has a periodicity of 52.4, 73.4, and 146.8 weeks. This result indicates that dengue will periodically appear at least every year in Jakarta. Parameter estimation for our model parameters was carried out by assuming the infection rate of humans as a sinusoidal function by determining the three most dominant frequencies. Numerical and sensitivity analyses were conducted to observe the impact of community ignorance on dengue endemicity. From the sensitivity analysis, we found that, although a larger community ignorance can trigger a backward bifurcation, this threshold can be minimized by increasing the recovery rate, prolonging the temporal immunity, or reducing the mosquito population. Therefore, to control dengue transmission more effectively, media campaigns undertaken by the government to reduce community ignorance should be accompanied by other interventions, such as a good treatment in the hospital or vector control programs. With this combination of interventions, it will be easier to achieve a condition of dengue-free population when the basic reproduction number is less than one.

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Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach

Cited by 21 publications

References 33 publications

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

Modeling the Impact of Vaccination on Epidemic Disease Variants with Hospitalization: A Case Study for the COVID-19 Pandemic in Turkey

Mathematical analysis of the impact of community ignorance on the population dynamics of dengue

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