RESUMO
Abstract In this paper, we present a new mathematical model to describe the evolution of the COVID-19 in countries under the state of emergency. Where the COVID-19 pandemic is sweeping country after country. The Italian and Moroccan authorities have declared a state of emergency in response to the growing threat of this novel coronavirus (COVID-19) outbreak by March 09 and 20, respectively. In-state of emergency, citizens cannot go out to public spaces without special authorization from local authorities. But after all these efforts exerted by these authorities, the number of new cases of the COVID-19 continues to rise significantly, which confirms the lack of commitment of some citizens. First, we aim to investigate the cause of new infections despite all strategies of control followed in these countries including media reports, awareness, and treatment, self-distancing and quarantine, by estimating the number of these people who underestimate the lives and safety of citizens and put them at risk. To do this, we use real data of the COVID-19 in Italy and Morocco to estimate the parameters of the model, and then we predict the number of these populations. Second, we propose an optimal control strategy that could be the optimal and the efficient way for the Moroccan and Italian authorities and other countries to make the state of emergency more efficient and to control the spread of the COVID-19. The model is analyzed for both countries and then to compare the implications of the obtained results. Numerical examples are provided to illustrate the efficiency of the strategy of control that we propose and to show what would have been happened in Morocco and Italy if this strategy of control was applied early.
RESUMO
Pharmacokinetics (PK) is the science of the kinetics of drug absorption, distribution and elimination. Statistical methods are usually used for PK parameter estimation producing nonlinear responses where drug effect mechanism is modeled using compartmental approach. In the present study, PK parameters were estimated with nonlinear fixed effects one compartment open model where drug dose and sampling time are covariates and the plasma drug concentration is dependent variable. The PK parameters namely absorption rate constant (a), elimination rate constant (b) and apparent volume of distribution (V) were estimated using nonlinear least square method for each individual separately and for all individuals collectively with longitudinal or multiple response plasma drug concentration-time data obtained from 24 healthy human volunteers with reference drug product of Atorvastatin. The estimates for combined data were â =0.13±0.13hr-1, =0.49±0.13hr-1, =248±0.05L. All the individuals were again stratified into three categories based on Body Mass Index (BMI) and the PK parameters were estimated for each stratum accordingly (stratum-normal: â=0.12±0.17hr-1, =0.47±0.17hr-1, =250.24±0.07L; stratum-overweight: â =0.15±0.24hr-1, =0.47±0.25hr-1, =267.25±0.09L; stratumunderweight: â =0.13±0.13hr-1, =0.49±0.13hr-1, =245±0.05L).