Abstract. This paper discusses the control of infectious diseases in the framework of optimal control approach. A case study on cholera control was studied by considering two control strategies, namely education and chlorination. We distinct the former control into one regarding person-to-person behaviour and another one concerning person-to-environment conduct. Model are divided into two interacted populations: human population which follows an SIR model and pathogen population. Pontryagin maximum principle was applied in deriving a set of differential equations which consists of dynamical and adjoin systems as optimality conditions. Then, the fourth order Runge-Kutta method was exploited to numerically solve the equation system. An illustrative example was provided to assess the effectiveness of the control strategies toward a set of control scenarios.
This paper is concerned with the inherentℋ2tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.
Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes .It can also be transmitted from an infected mother (congenitally) or through blood transfusion. In this paper, we discussed the transmission of malaria featuring in the framework of an SIRS-SI model with treatments are given to humans and mosquitoes. We here utilized the use of vaccines, the use of anti-malarial drugs, and the use of spraying as treatment efforts. A stability analysis was then performed and numerical simulation was provided to clarify the result. It is shown that treatments affect the dynamics of human and mosquito populations. In addition, we proposed the Homotopy Analysis Method (HAM) to construct the approximate solution of the model.
Improving services through goods pickups and deliveries to expand the market is currently being carried out by many companies. This effort needs another step of optimization to avoid losses due to additional resources, such as time, which must be held by the company. In the case of simultaneous goods pickups and deliveries using a vehicle with single transport access, the policy of arranging goods in the vehicle can affect the length of time for service. Single transport access causes goods that want to be unloaded obstructed by the other goods, thus requires additional time for handling. In this paper, the problem of a vehicle’s route and handling time in picking and delivering goods with time windows is modeled as the Traveling Salesman Problem. The objective function of this problem is to minimize the total travel time and handling time during the picking and delivering goods. The model is implemented in the case of bicycle pickup and delivery services involving 15 bicycle shops. The capacity of the vehicle is 15 units of bicycle. In this case, a solution consisting the pickup and delivery route and optimal goods order is obtained with an objective function value of 334 minutes.
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