The development of a deterministic dengue epidemic model with the influence of temperature: A case study in Malaysia

Hamdan, Nur ’Izzati; Kılıçman, Adem

doi:10.1016/j.apm.2020.08.069

Cited by 19 publications

(9 citation statements)

References 34 publications

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“…Instead, it is determined by the effective distance from the outbreak site to different destinations. Even if the epidemiological parameters of an epidemic are unknown, the effective distance can be used to predict the relative arrival time of the epidemic [ 4 – 8 ]. In this study, the linear relationship between the effective distance and the arrival time of COVID-19 has been demonstrated.…”

Section: Discussionmentioning

confidence: 99%

A Linear Regression Prediction Model of Infectious Disease Spread Based on Baidu Migration and Effective Distance

Zhou

2022

Computational and Mathematical Methods in Medicine

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Objective. To analyze the relationship between effective distance and epidemic spread trajectory and between arrival time and scale based on the COVID-19 data outbreak in Wuhan and thus to improve the prediction ability of the spread of infectious disease. Methods. Up to January 28, 2020, the reporting date, the onset date, and the cumulative number of confirmed cases of COVID-19 in each province and city were collected. Baidu migration data was used to calculate the effective distance from Wuhan city to other regions. The reporting date and onset date of the first diagnosed patient were taken as the arrival time, respectively, to establish a linear regression model of effective distance and arrival time. In different provinces and cities, the logarithm of the cumulative number of confirmed cases with a base of 5 was taken as the criteria to determine the level of the cumulative confirmed cases. Based on this, the linear regression model of effective distance and the level of cumulative confirmed cases in the provincial and municipal units was established. Results. The linear correlation between the reporting date of the first confirmed patient and the effective distance was not strong. The coefficients of determination ( R 2 ) for cities with and without the cities of Hubei Province were 0.36 and 0.44, respectively. And the linear correlation between the onset date of the first confirmed patient and the effective distance was strong. And the coefficients of determination ( R 2 ) for cities with and without the cities of Hubei Province were 0.67 and 0.83, respectively. And the linear correlation between the level of cumulative confirmed cases in the provincial and municipal units and the effective distance was strong, with an R 2 of 0.87 and 0.84, respectively. The regression coefficients of each linear model were statistically significant ( P < 0.001 ). Conclusion. The effective distance has a good fit with the model of the onset date of the first confirmed patient and the level of cumulative confirmed cases, which can predict the trajectory, time, and transmission range of the epidemic. It can be taken as the reference for the early warning, prevention, and control of sudden acute infectious diseases from a macro perspective.

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Section: Discussionmentioning

confidence: 99%

A Linear Regression Prediction Model of Infectious Disease Spread Based on Baidu Migration and Effective Distance

Zhou

2022

Computational and Mathematical Methods in Medicine

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“…In this situation, we conclude that ensuring the size of the basic reproduction number to be <1 does not always guarantee the disappearance of dengue. Several authors have shown the appearance of a backward bifurcation in the dengue transmission model in their models [56][57][58][59]. Their analysis showed that some crucial aspects were not included in the calculation of the basic reproduction number.…”

Section: Summary and Concluding Remarksmentioning

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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“…This approach has two main disadvantages 48 . An elegant solution to these problems is to avoid the use of Riemann–Liouville derivatives and to use Caputo fractional derivatives 49 . This technique was defined as follows:

D_{* α}^{α} x (t) = \frac{1}{normalΓ (n - α)} \int_{a}^{t} \frac{d^{n}}{d τ^{n}} f (τ) {MathClass-open(t - τ MathClass-close)}^{n - α - 1} d τ,

where,

α

is the order of the derivative with

n - 1 < α < n

and

n = [α] + 1, normalΓ (n - α)

is the Euler gamma function.…”

Section: Fractional Compartmental Model Of Jementioning

confidence: 99%

A comparative series solutions of Japanese encephalitis model using differential transform method and variational iteration method

Baniya

Keval

2021

Heat Trans

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In this study, a deterministic mathematical model involving the transmission dynamics of Japanese encephalitis (JE) is presented and studied. The biologically feasible equilibria and their stability properties have been discussed. This study investigates a series of solutions to the system of ordinary differential equations (ODEs) in the transmission dynamics of JE. To get approximate series solutions of the JE model, we employed the differential transform method (DTM) and variational iteration method (VIM). DTM utilizes the transformed function of the original JE model, while VIM uses the general Lagrange multiplier to develop the correction functional for the JE model. The results show that the VIM solution is more accurate than the DTM solution for short intervals of time. In addition, the fractional compartmental model of JE is briefly discussed. We illustrated the profiles of the solutions of each of the compartments, from which we found that the fourth‐order Runge–Kutta method solutions are more accurate than the DTM and VIM solutions for long intervals of time.

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The development of a deterministic dengue epidemic model with the influence of temperature: A case study in Malaysia

Cited by 19 publications

References 34 publications

A Linear Regression Prediction Model of Infectious Disease Spread Based on Baidu Migration and Effective Distance

A Linear Regression Prediction Model of Infectious Disease Spread Based on Baidu Migration and Effective Distance

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

A comparative series solutions of Japanese encephalitis model using differential transform method and variational iteration method

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