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Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned factors. In the present paper, we study a discrete age continuous mathematical model that describes the dynamics of diabetics. We highlight the negative impact of socio-environmental on diabetic patients according to age groups. We also suggest an optimal strategy to implement the best campaigns of rising awareness that aims at protecting diabetic patients from the negative impact of a lifestyle that leads them to complications. In addition to psychological treatment and follow-up of diabetic patients with complications, an awareness campaign will also be carried out for people with potential diabetes that aims at educating them about the dangerous of diabetes and its complications. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, structure-preserving model reduction methods for second-order systems are investigated. By introducing an appropriate parameter, the second-order system is represented by a strictly dissipative realization and the H2 norm of the strictly dissipative system is discussed. Then, based on the Krylov subspace techniques, two model reduction methods are proposed to reduce the order of the strictly dissipative system. Further, the reduced second-order systems are obtained. Moreover, according to the factorization of the error system, the H2 error bounds are represented by the Kronecker product and the vectorization operator. Finally, two numerical examples illustrate the efficiency of our methods. [ABSTRACT FROM AUTHOR]

This paper proposes an identification method for estimating the parameters of a stable second-order system based on the impulse response experiment. From the impulse response experiment, the measured data are collected for implementing parameter estimation. By defining and minimizing a cost function, a Newton iterative algorithm is derived for estimating the parameters of the system. The multi-point identification method is used to show the effectiveness of the proposed Newton iterative algorithm. The results show that the estimated model by the proposed Newton iterative estimation method has higher accuracy. Based on the estimated model, a design method of the proportional derivative controller is presented according to the system dynamical performance. The simulation test shows that the proposed controller design method can meet the desired dynamic specifications. [ABSTRACT FROM AUTHOR]

In this study, we have investigated local and global dynamics of a modified Leslie–Gower predator–prey model with Monod–Haldane functional response, where prey is subjected to quadratic harvesting. It is found that the solutions of the proposed system are positive and bounded uniformly. The feasible equilibrium points are also obtained for some suitable and predefined conditions. It is observed that the system exhibits at most three non-zero interior equilibrium points for different choices of parameters under certain conditions. The dynamics of all these feasible equilibrium points have been analysed using Routh–Hurwitz criterion. Local bifurcations analysis such as transcritical and saddle-node bifurcations have been investigated using Sotomayor's theorem. To demonstrate the analytical results, numerical simulations using some suitable data set are carried out. Optimal harvesting policy has been obtained using Pontryagin's Maximum Principle to show that the species can be preserved from extinction and a sustainable fishery can be achieved. [ABSTRACT FROM AUTHOR]

We study in this work a discrete mathematical model that describes the dynamics of transmission of the Corona virus between humans on the one hand and animals on the other hand in a region or in different regions. Also, we propose an optimal strategy to implement the optimal campaigns through the use of awareness campaigns in region j that aims at protecting individuals from being infected by the virus, security campaigns and health measures to prevent the movement of individuals from one region to another, encouraging the individuals to join quarantine centers and the disposal of infected animals. The aim is to maximize the number of individuals subjected to quarantine and trying to reduce the number of the infected individuals and the infected animals. Pontryagin's maximum principle in discrete time is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using Matlab. The Incremental Cost-Effectiveness Ratio was calculated to investigate the cost-effectiveness of all possible combinations of the four control measures. Using cost-effectiveness analysis, we show that control of protecting susceptible individuals, preventing their contact with the infected individuals and encouraging the exposed individuals to join quarantine centers provides the most cost-effective strategy to control the disease. [ABSTRACT FROM AUTHOR]

A transmission and control model for measles infection is presented. The model incorporates vaccinated individuals and the role of treatment for both exposed and infected individuals. We present two main equilibrium points (disease-free and endemic) with the analysis of their stability. The basic reproduction number is calculated and we find that when it is less than unity, the disease-free equilibrium point is both locally and globally stable which means the disease can be eradicated under such condition. When it is greater than one, the infection is uniformly persistent and the endemic equilibrium is globally stable. The sensitivity index of basic reproduction number to the parameters within the model is also determined. Further, by using Pontryagin's minimum principle, the optimal control problem is constructed with three controls i.e. vaccination, treatment of exposed individuals and treatment of infected individuals. Finally, the numerical simulations are established and our results show that a combination of all three controls gives the best result in reducing the number of measles infected individuals. These results indicate that being vaccinated followed by some treatments for both exposed and infected individuals would make measles eradication more efficient. [ABSTRACT FROM AUTHOR]

In this article, the global dynamics of a predator–prey system incorporating combined harvesting has been investigated. The additional food is being provided to the predator, accordingly, modified Holling type-II functional response is considered in the model. The presence of toxicants affect the quality of food for both the species, reducing their growth. The steady states of the system are obtained under some suitable conditions. The local and global dynamics are explored. The conditions for permanence and existence for bionomic equilibrium of the system have been investigated. It is also observed that the system exhibits local bifurcations i.e., transcritical, Hopf, saddle-node as well as global bifurcations i.e., Bogdanov–Takens bifurcation and generalized Hopf bifurcation with respect to the suitable set of parameters. Optimal harvesting policy is discussed with the help of Pontryagin's maximum principle to preserve both the species from extinction and maintain a sustainable fishery. Numerical simulations are carried out for the suitable choice of parameters. [ABSTRACT FROM AUTHOR]

Jatropha curcas plant is seriously affected by the mosaic disease caused by begomovirus which is carried through infected white-flies. It severely affects the Jatropha plants causing leaf damage, yellowing leaves and sap drainage. Traditionally, the diseased is controlled by roguing or removal of infected plant biomass, using insecticides or increasing resistance to host plant. In this article, a mathematical model is formulated to study mosaic disease dynamics in J. curcas plantations with roguing. Also, time delay has been incorporated in roguing and reformulates the mathematical model using delay differential equations. Sufficient conditions for the stability of the equilibrium points of the system are among the results obtained through qualitative analysis. Using the normal form theory and the center manifold theorem, the stability and direction of the bifurcating periodic solutions of the delayed system are determined. The findings are confirmed by means of numerical simulations. [ABSTRACT FROM AUTHOR]