Optimal control problem on COVID-19 disease transmission model considering medical mask, disinfectants and media campaign

Aldila, Dipo

doi:10.1051/e3sconf/202020212009

Cited by 8 publications

(7 citation statements)

References 21 publications

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“…To construct the basic reproduction (1), we use the next-generation matrix approach [29]. The reader may see [30,31,32,33,34,35,36] for another example of the derivation of  0 using this method.…”

Section: The Disease-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

Optimal control problem and backward bifurcation on malaria transmission with vector bias

Aldila

Angelina

2021

Heliyon

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This article aims to apply a mathematical model to investigate the spread of malaria by considering vector bias, saturated treatment, and an optimal control approach. A mathematical analysis of the equilibrium points and an investigation of the basic reproduction number show that if the basic reproduction number ( is less than one, the disease-free equilibrium is locally asymptotically stable. Furthermore, the center-manifold theory is applied to analyze the stability of the endemic equilibrium when 1 . We find that our model performs a backward bifurcation phenomenon when the saturated treatment or vector bias parameter is larger than the threshold. Interestingly, we found that uncontrolled fumigation could increase the chance of the appearance of backward bifurcation. From the sensitivity analysis of , we find that the fumigation and vector bias are the most influential parameters for determining the magnitude of . Using the Pontryagin maximum principle, the optimal control problem is constructed by treating fumigation and medical treatment parameters as the time-dependent variable. Our numerical results on the optimal control simulation suggest that time-dependent fumigation and medical treatment could suppress the spread of malaria more efficiently at minimum cost.

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Section: The Disease-free Equilibrium and The Basic Reproduction Numbermentioning

confidence: 99%

Optimal control problem and backward bifurcation on malaria transmission with vector bias

Aldila

Angelina

2021

Heliyon

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“…Several models proposed in these papers do not take into account the indirect transmission. The impact of non-pharmaceutical aproach on the spread of covid-19 is discussed in [11], [12], [15], [18]. Some of these papers also present optimal control problem [11][12][13][14], [16], [18].…”

Section: Introductionmentioning

confidence: 99%

Stability, cost-effectiveness, and global sensitivity analysis of COVID-19 model incorporating non-pharmaceutical interventions and indirect transmission

Darmawati

Nur

2022

DAAM

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Covid-19 is an ongoing pandemic caused by SARS-CoV-2. Some interventions are implemented to control the spread of the disease. In Indonesia, there is a campaign related to non-pharmaceutical approach called 3M. This campaign is carried out so that people use masks, wash their hands, and keep their distance. In this paper, we propose a mathematical model considering non-pharmaceutical interventions and indirect transmission. The non-pharmaceutical interventions studied are the implementation of mask-wearing, handwashing, and social distancing. The model is presented as a system of first-order differential equations. The basic reproduction number is determined. The system has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The local stability condition of the disease-free equilibrium point is proved using the Lienard-Chipart criterion. Center manifold theory is used to prove the local stability condition of the endemic equilibrium point. We also study the optimal control strategy related to mask-wearing, handwashing, and social distancing. Furthermore, cost-effectiveness analysis of intervention strategies is also conducted by studying the average cost-effectiveness ratio of each intervention strategy. Our results show that the most effective strategy to control covid-19 spread is the combination of mask-wearing, handwashing, and social distancing. Moreover, the most cost-effective strategy is mask-wearing intervention. Global sensitivity analysis is performed by studying the partial rank correlation coefficient. The results show that mask-wearing intervention is the most influential intervention on basic reproduction number compared to social distancing and handwashing

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“…The symptoms of COVID-19 resemble those of ordinary flu but could lead to death as a consequence of the difficulty in breathing for patients in advanced stages. Till now, there is no medicine to cure infected individuals [3].…”

Section: Introductionmentioning

confidence: 99%

“…Due to the limited availability of vaccines in the community, the most popular and effective way to control the spread of COVID-19 is to prevent infection through non-pharmaceutical interventions such as physical distancing, use of medical masks, quarantine, use of disinfectants, contact tracing, etc. [3]. Among the strategies implemented the most to minimize the risk of infection are social distancing and the use of medical masks.…”

Section: Introductionmentioning

confidence: 99%

“…Many approaches have been used by these authors such as ordinary differential equations [5], [6], [7], [8], [9], partial differential equation [11], statistics [12], [13], [14], artificial intelligence and optimal control approaches [15], [16]. Their research has covered several important factors such as the impact of vaccination [10], social distancing [1], [17], hospitalization [18], contact tracing [18], [19], and social awareness [2], [3], [4], [17]. From the previously mentioned literature, several important results are presented.…”

Section: Introductionmentioning

confidence: 99%

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Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model

Balya

Dewi

Lestari

et al. 2021

CBMS

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In this article, we propose and analyze a mathematical model of COVID-19 transmission among a closed population, with social awareness and rapid test intervention as the control variables. For this, we have constructed the model using a compartmental system of the ordinary differential equations. Dynamical analysis regarding the existence and local stability of equilibrium points is conducted rigorously. Our analysis shows that COVID-19 will disappear from the population if the basic reproduction number is less than one, and persist if the basic reproduction number is greater than one. In addition, we have shown a trans-critical bifurcation phenomenon based on our proposed model when the basic reproduction number equals one. From the elasticity analysis, we have observed that rapid testing is more promising in reducing the basic reproduction number as compared to a media campaign to improve social awareness on COVID-19. Using the Pontryagin Maximum Principle (PMP), the characterization of our optimal control problem is derived analytically and solved numerically using the forward-backward iterative algorithm. Our cost-effectiveness analysis shows that using rapid test and media campaigns partially are the best intervention strategy to reduce the number of infected humans with the minimum cost of intervention. If the intervention is to be implemented as a single intervention, then using solely the rapid test is a more promising and low-cost option in reducing the number of infected individuals vis-a-vis a media campaign to increase social awareness as a single intervention.

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Optimal control problem on COVID-19 disease transmission model considering medical mask, disinfectants and media campaign

Cited by 8 publications

References 21 publications

Optimal control problem and backward bifurcation on malaria transmission with vector bias

Optimal control problem and backward bifurcation on malaria transmission with vector bias

Stability, cost-effectiveness, and global sensitivity analysis of COVID-19 model incorporating non-pharmaceutical interventions and indirect transmission

Investigating the Impact of Social Awareness and Rapid Test on A COVID-19 Transmission Model

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