In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment, and educational campaign as time-dependent control functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and Pontryagin’s maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with the fourth-order Runge–Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that effective educational campaigns and vaccination of susceptible individuals as well as effective treatments of infected individuals can help reduce the disease transmission.

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In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola infection using vaccination, treatment and educational campaign as time-dependent controls functions. We have applied indirect methods to study existing deterministic optimal control epidemic models for Ebola virus disease. These methods in optimal control are based on Hamiltonian function and the Pontryagin's maximum principle to construct adjoint equations and optimality systems. The forward-backward sweep numerical scheme with fourth-order Runge-Kutta method is used to solve the optimality system for the various control strategies. From our numerical illustrations, we can conclude that, effective educational campaigns and vaccination of susceptible individuals as were as effective treatments of infected individuals can help reduce the disease transmission.

No abstract

Time in the twenty-first century plays an integral part in every sphere of our daily activities; this key factor in life is not an exception to solid waste management operators, whose operational cost account for about 80% of their total cost. In this paper, adopted the classical Vehicle Routing Problem with Time Window and enhanced it with two additional factors, such as the vehicle breaking distance/time which is absent in VRPTW and individual customer service time which is assumed to be constant in VRPTW. The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at the depot, and the total demands of all customers on one particular route must not exceed the capacity of the vehicle. Our enhanced VRPTW was applied to a real world problem in Tafo Pankrono and compared with the existing collection time by the waste management company in the area (Zoom Lion Company Limited). Our enhanced model saw a drastic reduction of 39% collection time as compared with the existing collection time.