Lyapunov stability analysis and optimization measures for a dengue disease transmission model

Abidemi, Afeez; Ackora-Prah, Joseph; Fatoyinbo, Hammed Olawale; Asamoah, Joshua Kiddy K.

doi:10.1016/j.physa.2022.127646

Cited by 25 publications

(6 citation statements)

References 35 publications

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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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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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“…That is, . Following the approach 1 , 34 , 63 , 64 , we consider the potential Lyapunov function constructed below. with Lyapunov Caputo derivative, …”

Section: Stability Analysis Of the Modelmentioning

confidence: 99%

Analysis of a non-integer order mathematical model for double strains of dengue and COVID-19 co-circulation using an efficient finite-difference method

Obiajulu,

Omame,

Inyama

et al. 2023

Sci Rep

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An efficient finite difference approach is adopted to analyze the solution of a novel fractional-order mathematical model to control the co-circulation of double strains of dengue and COVID-19. The model is primarily built on a non-integer Caputo fractional derivative. The famous fixed-point theorem developed by Banach is employed to ensure that the solution of the formulated model exists and is ultimately unique. The model is examined for stability around the infection-free equilibrium point analysis, and it was observed that it is stable (asymptotically) when the maximum reproduction number is strictly below unity. Furthermore, global stability analysis of the disease-present equilibrium is conducted via the direct Lyapunov method. The non-standard finite difference (NSFD) approach is adopted to solve the formulated model. Furthermore, numerical experiments on the model reveal that the trajectories of the infected compartments converge to the disease-present equilibrium when the basic reproduction number ($${\mathbb {R}}_0$$ R 0 ) is greater than one and disease-free equilibrium when the basic reproduction number is less than one respectively. This convergence is independent of the fractional orders and assumed initial conditions. The paper equally emphasized the outcome of altering the fractional orders, infection and recovery rates on the disease patterns. Similarly, we also remarked the importance of some key control measures to curtail the co-spread of double strains of dengue and COVID-19.

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“…Optimal control has become an effective tool in modeling the dynamics of different infectious diseases [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] . Khan et al.…”

Section: Introductionmentioning

confidence: 99%

“…Abidemi et al. [40] adopted Lyapunov stability analysis and optimal control measures in mitigating dengue disease transmission. Recently, Ojo et al.…”

Section: Introductionmentioning

confidence: 99%

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control

Omame

Abbas

2023

Physica A: Statistical Mechanics and its Applications

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Lyapunov stability analysis and optimization measures for a dengue disease transmission model

Cited by 25 publications

References 35 publications

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

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

Analysis of a non-integer order mathematical model for double strains of dengue and COVID-19 co-circulation using an efficient finite-difference method

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control

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