Absorbing Markov chains for analyzing COVID-19 infections

Recently, there are many works that proposed modeling approaches to describe the random movement of individuals for COVID-19 infection. However, these models have not taken into account some key aspects for disease such the prediction of expected time of patients remaining at certain health state before entering an absorption state (e.g., exit out of the system for ever such as death state or recovery). Therefore, we propose a dynamical model approach called the absorbing Markov chains for analyzing COVID-19 infections. From this modeling approach, we seek to focus and predict two states of absorption: recovery and death, as these two conditions are considered as important indicators in assessment of the health level. Based on the absorbing Markov model, the study suggested that there is a gradually increase in the predicted death number, while a decrease in the number of recovered individuals.

Ethics and Education

Education is a frequent area of concern when attempting to improve organizational performance. In this paper, absorbing Markov chains were used to assess education levels of civil servants within Air Force Materiel Command (AFMC). The results suggest that AFMC will have 47% of its workforce with an advanced, college degree by the year 2030. Given an increasingly educated workforce within AFMC, ethical implications for management strategy were explored. Specifically, the authors examined the ethics of managing a highly-educated workforce in ways which are procedurally similar to those used for a workforce which was historically less educated. Through a thematic bifurcation, ethical solutions were presented which will either provide more autonomy for the highly-educated workforce or attempt to change the internal credentialing process so that the current management strategies are aligned to a more appropriately-educated workforce.

Improving Graduation Rate Estimates Using Regularly Updating Multi-Level Absorbing Markov Chains

American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students’ final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a frequentist approach is used. For the standard six-year graduation rate method, the frequentist approach corresponds to counting the number of students who finished their program within six years and dividing by the number of students who entered that year. In the case of absorbing Markov chains, the frequentist approach is used to compute the underlying transition matrix, which is then used to estimate the graduation rate. In this paper, we apply a sensitivity analysis to compare the performance of the standard six-year graduation rate method with that of absorbing Markov chains. Through the analysis, we highlight significant limitations with regards to the estimation accuracy of both approaches when applied to small sample sizes or cohorts at a university. Additionally, we note that the Absorbing Markov chain method introduces a significant bias, which leads to an underestimation of the true graduation rate. To overcome both these challenges, we propose and evaluate the use of a regularly updating multi-level absorbing Markov chain (RUML-AMC) in which the transition matrix is updated year to year. We empirically demonstrate that the proposed RUML-AMC approach nearly eliminates estimation bias while reducing the estimation variation by more than 40%, especially for populations with small sample sizes.

On the Structure of the World Economy: An Absorbing Markov Chain Approach

The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries’ positioning in global value chains. We are approaching the structure and lengths of value chains from a completely different perspective than has been available so far. By assigning a random endogenous variable to a network linkage representing the number of intermediate sales/purchases before absorption (final use or value added), the discrete-time absorbing Markov chains proposed here shed new light on the world input/output networks. The variance of this variable can help assess the risk when shaping the chain length and optimize the level of production. Contrary to what might be expected simply on the basis of comparative advantage, the results reveal that both the input and output chains exhibit the same quasi-stationary product distribution. Put differently, the expected proportion of time spent in a state before absorption is invariant to changes of the network type. Finally, the several global metrics proposed here, including the probability distribution of global value added/final output, provide guidance for policy makers when estimating the resilience of world trading system and forecasting the macroeconomic developments.

Ethics and Education

Education is a frequent area of concern when attempting to improve organizational performance. In this paper, absorbing Markov chains were used to assess education levels of civil servants within Air Force Materiel Command (AFMC). The results suggest that AFMC will have 47% of its workforce with an advanced, college degree by the year 2030. Given an increasingly educated workforce within AFMC, ethical implications for management strategy were explored. Specifically, the authors examined the ethics of managing a highly-educated workforce in ways which are procedurally similar to those used for a workforce which was historically less educated. Through a thematic bifurcation, ethical solutions were presented which will either provide more autonomy for the highly-educated workforce or attempt to change the internal credentialing process so that the current management strategies are aligned to a more appropriately-educated workforce.