Developing a detection model for a COVID‐19 infected person based on a probabilistic dynamical system

Abstract

This paper presents a novel model to detect the COVID‐19 infected person from a Markovian feedback persons in a limited department capacity. The persons arrive one by one to the department and the balking and the retention of reneged person approaches are considered. There exists one server presents the service to these persons according to first‐come, first‐served (FCFS) discipline. An efficient and novel algorithm is presented to get the exact value of the probability of n persons in the department at any time interval. This algorithm depends on the Laplace transform to solve a probabilistic dynamical system of differential equations. By considering the exponential detection function and if the probability of the infected person in the department is equal to the probability of each one, then this algorithm is useful to obtain the detection probability of the infected one. Under steady state, the detection probability of the infected person is described. The usefulness of this model is illustrated for different capacities by using a numerical example to describe the behavior of probabilities of the persons in the department, the detection probabilities of the infected person as functions in time, and the mean time to detection.

Detection Model With a Maximum Discounted Effort Reward Search to Maintenance a Best Decision Under the Quality Control Process

“…To achieve these criteria, it is necessary to find the optimal values Z * niσ , µ * iσ , and (ϖ σ i ) * . These values can be found by solving (27). We consider the values of λ iσ , n iσ , C i , and N i are generated randomly by using Maple 13 as in Table 1.…”

“…, which have been obtained in [1] (values without discount effort-reward). Using these values in (27), one can get the maximum probability of n iσ customers in the company Q i , which have several service channels C i = 4 at time step σ, σ = 2&4 see Table 1. The plotting 3D of (27) (Figure 2), presents the relationship between (ϖ σ σ ) * , and Z * nσ for different capacities N σ when σ = 2& 4, where all peaks of the cones give the needed optimal values which satisfied (27).…”

“…Using these values in (27), one can get the maximum probability of n iσ customers in the company Q i , which have several service channels C i = 4 at time step σ, σ = 2&4 see Table 1. The plotting 3D of (27) (Figure 2), presents the relationship between (ϖ σ σ ) * , and Z * nσ for different capacities N σ when σ = 2& 4, where all peaks of the cones give the needed optimal values which satisfied (27). By using Maple 13, we can obtain an equation of (ϖ σ σ ) * , and Z * nσ that present the needed optimal solution, see Figure 3.…”

“…[1] solved a difficult optimization problem under the steady-state situation to get a suitable company with the highest service rate. The search models for the lost targets vary according to the circumstances in which the searching process takes place, for example, [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]. The main purpose of these models is to find these targets with minimum cost and maximum probability.…”

Optimal Multi Zones Search Technique to Detect a Lost Target by Using K Sensors

“…The main purpose of these different techniques is finding the target in minimum cost and with maximum probability. More recent search models to detect the lost targets can be found in [44,45].…”