Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

As of November 14, 2020, the number of people infected with the COVID-19 disease has reached more than 54 million people worldwide and more than 1323196 people have died, according to the World Health Organization. This requires many countries to impose a health emergency or quarantine, which has had positive results in reducing the spread of the COVID-19 pandemic, and it has also had negative economic, social and health effects. So, we suggest a mathematical model for the dynamics of how COVID-19 disease is spread, as well as a mathematical modeling for the dynamics of diabetes, then highlight the negative effect of quarantine has on the health of diabetics. Pontryagin’s maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.

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“…For

the adjoint equations and transversality conditions can be obtained by using Pontryagin’s maximum principle [38] , [39] , [40] , [41] such that

…”

Section: The Optimal Control: Existence and Characterizationmentioning

confidence: 99%

Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness

Kouidere

Youssoufi

Ferjouchia

et al. 2021

Chaos, Solitons & Fractals

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“…Recent studies reported that between 2 and 14 days can elapse from the day of SARS-CoV-2 infection and the appearance of the first disease symptoms (incubation period) (Kouidere et al 2020;Lee et al 2020;Huang et al 2020). Thus, if SARS-CoV-2 were transported in particulate material, an increase of infection cases should be observed after contamination events.…”

Section: Effect Of Meteorological Parameters On Pm 25 and Pm 10mentioning

confidence: 99%

PM10 correlates with COVID-19 infections 15 days later in Arequipa, Peru

Wannaz

Valdivia

Larico

et al. 2021

Environ Sci Pollut Res

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The emergence of COVID-19 and the spread of this novel disease around the world in 2020 has entailed several cultural changes; some of those changes are positive for the environment, such as the decrease in the concentration of atmospheric particulate matter. We compared the concentrations of PM 2.5 and PM 10 recorded in October and November 2019 (pre-pandemic period) with the concentrations recorded from May to October 2020 (pandemic period) in the city of Arequipa, Peru. A significant decrease in the concentration of PM 2.5 (less than 21.0%) and PM 10 (less than 21.5%) was observed on Sundays, when population movement was strongly restricted. First, we observed a significant correlation between PM 2.5 and PM 10 concentration in the atmosphere and the number of infections reported in Arequipa, Peru. However, when we removed the data of Sundays from the database, these correlations were no longer significant. Subsequently, we correlated PM 2.5 and PM 10 concentrations with the number of COVID-19 infections on the same day and up to a 20-day delay and found that from day 15 to day 18, PM 10 concentration was significantly correlated with COVID-19 infections, suggesting that SARS-CoV-2 might circulate attached to the coarse particle (PM 10) and that this fraction would act as infection vector. However, these results may reflect other factors, such as social or economic factors that could explain the dynamics of infection in Arequipa, Peru. Further research is needed to better understand the dynamics of the SARS-CoV-2 pandemic.

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“…A new proposed model is given in [ 9 ] to simulate the new cases and deaths of the virus outbreak in India. The study of the virus impact in Brazil through a multiple-delay mathematical model and the optimal control strategies is illustrated in [ 10 ]. Other relative studies of integer-order models can be found in [ 11 , 12 ].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

et al. 2021

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In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different compartments in their environments. The equilibrium points of the new system are found for both diffusive and non-diffusive models, where a detailed stability analysis is conducted for them. Moreover, the stability regions in the space of parameters are attained for each equilibrium point for both cases of the model and the effects of parameters are explored. A numerical verification for the proposed model using a finite difference-based method is illustrated along with their consistency, stability and proving the positivity of the acquired solutions. The obtained results reveal that the random motion of individuals has significant impact on the observed dynamics and steady-state stability of the spread of the virus which helps in presenting some strategies for the better control of it.

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Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

Abstract: Highlights We propose to study an optimal control approach with delay in state and control variables. Numerical simulation of different strategies. The cost of effectivness.

Cited by 36 publications

References 20 publications

Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness

Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness

PM10 correlates with COVID-19 infections 15 days later in Arequipa, Peru

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

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