Markovian Analysis of Covid-19 Dynamics

Abstract:

Covid-19 is an emergency and viral infection with its outbreak being termed as one of the great epidemics in the 21st century causing so many deaths, which made WHO declare it as a pandemic emergency. This virus is new and comes with its characteristics of which randomness and uncertainty are among its common features. In this paper, we developed a model for carrying out an analysis of COVID-19 dynamics using Markov-chain theory methodology. Here, we employed the use of conditional probability distribution as embedded in the Markov property of our chain to construct the transition probabilities that were used in determining the probability distributions of COVID-19 patients as well as predicting its future spread dynamics. We provide a step-by-step approach to obtaining probability distributions of infected and recovered individuals, of infected and recovering and of a recovered patient being getting infected again. This study reveals that irrespective of the initial state of health of an individual, we will always have probabilities P_RI/〖(P〗_IR+P_RI) of an individual being infected and P_RI/〖(P〗_IR+P_RI) of an individual recovering from this disease. Also, with increasing ‘n’, we have an equilibrium that does not depend on the initial conditions, the implication of which is that at some point in time, the situation stabilizes and the distribution X_(n+1) is the same as that of X_n. We envision that the output of this model will assist those in the health system and related fields to plan for the potential impact of the pandemic and its peak.