ABSTRACT
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.
ABSTRACT
Recent studies showed that certain drugs can change regulatory reaction parameters in gene regulatory networks (GRNs) and therefore restore pathological cells to a normal state. A state control framework for regulating biological networks has been built based on attractors and bifurcation theory to analyze this phenomenon. However, the control signal is self-developed in this framework, of which the parameter perturbation method can only calculate the state transition time of cells with single control variable. Therefore, an optimal control method based on the dynamic optimization algorithms is proposed for complex biological networks modeled by nonlinear ordinary differential equations (ODEs). In this approach, dynamic optimization problems are constructed based on basic characteristics of the biological networks. Furthermore, using an example of a simple low-dimensional three-node GRN and a complex high-dimensional cancer GRN, MATLAB is utilized to calculate optimal control strategies with either single or multiple control variables. This method aims to achieve accurate and rapid state regulation for biological networks, which can provide a reference for experimental researches and medical treatment.
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In this paper, a nonlinear mathematical model is developed and analyzed to study the dynamics of Ebola virus (EVD) and the effects of some control strategies. The model validity is investigated and was found to be locally asymptotically stable when the basic reproduction number and unstable otherwise. Pontryagin's maximum principle is applied to obtain the optimality conditions. Numerical simulation was carried out and the results obtained indicate that a combination of all three control parameters is highly effective in containing the spread of the virus.
ABSTRACT
Objective:To analyze the economic growth effect of government health expenditure and discuss the optimal decision about the proportion of govemment health expenditure.Methods:Based on the endogenous growth model with family and government,the optimal control method was used to deduce and analyze the theoretical model.Results:The government health expenditure has a nonlinear relationship of the impact on economic growth,the critical value of the optimal proportion depended on the output share of healthy,the output share of productive capital and the contribution share of government health expenditure to healthy.Conclusion:The government should determine the reasonable proportion of health expenditure according to the stage of economic development.
ABSTRACT
Ebola virus is a severe, frequently fatal illness, with a case fatality rate up to 90%. The outbreak of the disease has been acknowledged by World Health Organization as Public Health Emergency of International Concern. The threat of Ebola in West Africa is still a major setback to the socioeconomic development. Optimal control theory is applied to a system of ordinary differential equations which is modeling Ebola infection through three different routes including contact between humans and a dead body. In an attempt to reduce infection in susceptible population, a preventive control is put in the form of education and campaign and two treatment controls are applied to infected and late-stage infected (super) human population. The Pontryagins maximum principle is employed to characterize optimality control, which is then solved numerically. It is observed that time optimal control is existed in the model. The activation of each control showed a positive reduction of infection. The overall effect of activation of all the controls simultaneously reduced the effort required for the reduction of the infection quickly. The obtained results present a good framework for planning and designing cost-effective strategies for good interventions in dealing with Ebola disease. It is established that in order to reduce Ebola threat all the three controls must be taken into consideration concurrently.
ABSTRACT
Este trabalho teve por objetivo geral propor e avallar técnicas de desenvolvimento de sistemas de controle automático para processos de tratamento de efluentes envolvendo lodos ativados. Os sistemas de controle propostos foram estabelecidos a partir da aplicação da Teoria de Controle Ótimo, considerando o emprego de um modelo dinâmico simplificado do processo de lodos ativados. Simulações computacionais foram utilizadas para a avaliação do desempenho dos sistemas de controle propostos. Os resultados obtidos permitiram concluir que o modelo dinâmico do processo de lodos ativados utilizado neste trabalho, estabelecido a partir de uma simplificação de modelo largamente aceito, segundo literatura técnica corrente, mostrou-se estável e adequado à definição de sistemas de controle.
This study aimed at developing and evaluating techniques for the development of automatic control systems for wastewater treatment systems involving activated sludge process. The proposed control systems were established from the application of Optimal Control Theory, considering the use of a simplified dynamic model of the activated sludge process. Computer simulations were used to assess the performance of the control systems proposed. The results showed that the dynamic model of the activated sludge process utilized in this study, obtained by simplifying a very well accepted model, according to the current technical literature, was stable and suitable for the definition of control systems.
ABSTRACT
Objective Impedance control plays an important role in stability.This paper intends to explore such mechanism through modeling human reaching movement.Method Implemented with revised model,we ap-ply optimal control theory to neuro-muscle-skeleton model to calculate the stiffness ellipses.Result Com-pared with the original model and experimental figures,the model we proposed could overcome the shortage of monotonous changing of the original one and fit the data better.Conclusions So that this paper concludes that co-contraction contributes to impedance control even during free upper limb planar movement.
ABSTRACT
Objective Impedance control plays an important role in stability.This paper intends to explore such mechanism through modeling human reaching movement.Method Implemented with revised model,we ap-ply optimal control theory to neuro-muscle-skeleton model to calculate the stiffness ellipses.Result Com-pared with the original model and experimental figures,the model we proposed could overcome the shortage of monotonous changing of the original one and fit the data better.Conclusions So that this paper concludes that co-contraction contributes to impedance control even during free upper limb planar movement.
ABSTRACT
Objective Impedance control plays an important role in stability.This paper intends to explore such mechanism through modeling human reaching movement.Method Implemented with revised model,we ap-ply optimal control theory to neuro-muscle-skeleton model to calculate the stiffness ellipses.Result Com-pared with the original model and experimental figures,the model we proposed could overcome the shortage of monotonous changing of the original one and fit the data better.Conclusions So that this paper concludes that co-contraction contributes to impedance control even during free upper limb planar movement.