A disease outbreak managing queueing system with self-generation of status and random clock for quarantine time

Sinu Lal T S, Varghese C. Joshua, Achyutha Krishnamoorthy
We propose an efficient model of an epidemic management system with the notion of self generation of status, and random clock for the quarantine period of a suspected person. The patient arrives according to a Markovian arrival process. They enter into a multi server station (casualty clinic) and the chance of a person suspected to be infected is p and he is sent to a quarantine pool; else (with probability 1-p), he leaves the system. For each customer in the quarantine pool, two random clocks start ticking upon his entry. One of the random clocks has Erlang distributed life time; this is the quarantine duration, on realization of which, the person can leave the system. On the other hand, a person in quarantine generates into being infected, in a time period from the time of his entry into the pool; this time duration has a Coaxian distribution. This is the second clock. The customer can leave the system upon the realization of the Erlang clock. The decision based on the clocks are: the customer can leave the system upon the realization of the Erlang clock, provided the Coxian clock does not realize until then. If the customer has generated the infected status before the realization of the Erlang clock (Coxian clock realizes before the Erlang clock), then he is transferred to the specially designed care unit of finite capacity. This system is modeled as a continuous time Markov chain and is analyzed using matrix analytic method. The main concern is on finding the optimal capacity of the care unit so that maximum number of infected are admitted, taking into consideration several risk factors.