We present a delay differential model with optimal control that describes the interactions of the tumour cells and immune response cells with external therapy. The intracellular delay is incorporated into the model to justify the time required to stimulate the effector cells. The optimal control variables are incorporated to identify the best treatment strategy with minimum side effects by blocking the production of new tumour cells and keeping the number of normal cells above 75% of its carrying capacity. Existence of the optimal control pair and optimality system are established. Pontryagin's maximum principle is applicable to characterize the optimal controls. The model displays a tumour-free steady state and up to three coexisting steady states. The numerical results show that the optimal treatment strategies reduce the tumour cells load and increase the effector cells after a few days of therapy. The performance of combination therapy protocol of immunochemotherapy is better than the standard protocol of chemotherapy alone.

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This paper describes a radar-guided monocular lead vehicle ahead of the host vehicle) starts to decelerate in vision system that detects, validates, and tracks the preceding order to perform a turn. Normally, in such scenario, drivers vehicle and thus predicts its lane-change intentions. A vision-have the ability to recognize that by the time they reach the based lane tracking process is developed to create a stable turning place, the primary vehicle should have already tuned motion model in order to map the radar targets to image away from their path. Also, drivers have the ability to adapt coordinates and consequently generate the region of interest their predictions based on the changes of host and target (ROI) to search for a potential preceding vehicle. Model-based a. b object classification algorithms are then applied to validate the ve le se It' mc esire if such palesfcanbe existence of a vehicle in this ROI. Once the detected primary added to ACC or FCW to enhance the system performance. target vehicle, which is in the same lane as the host vehicle, isIn this paper we present a system that uses the radar-cue validated, it will be continuously tracked until it leaves the host guided monocular vision process to validate the radar lane. The spatial-temporal tracking history of the primary detected targets and characterize the moving pattern of the target vehicle is used to infer its intention of changing lanes. in-lane primary target. The system aims to enhance the This prediction results from a characterization process for the performance of ACC and FCW. The objective of the target primary target motion vector. The radar-vision integrated validation is to decide if the target is indeed in the host system has been evaluated on real-world data collected using a vehicle lane and whether it represents an obstacle in the host test vehicle equipped with a radar sensor, vision sensor, and a vehicle path. Non-vehicle targets, such as overhead bridges host processor. and road signs are not considered to be the valid targets and thus will be ignored. The characterization task aims to predict if a primary target is leaving the host lane. A vehicle I. INTRODUCTION that is turning or leaving the host lane is considered to be a V ehicle control and driver awareness system such as target of low threat. In validation process, both moving and [Adaptive Cruise Control (ACC) or Forward Collision stationary targets are considered, whereas in characterization Warning (FCW) systems suffer from poor performance task, only primary moving targets are considered. when reacting to drivable stationary vehicles or precedingIn this radar-guided monocular vision system, vehicle (i.e. lead) vehicles that are turning or leaving the host vehicle validation and characterization are performed by using (the vehicle which hosts the ACC or FCW systems) lane. In pattern classification process on video data. The underlying case of ACC, braking as a result of detecting a stationary supporting video processing tasks involve real-time lane vehicle ...