Since the early days of the coronavirus (COVID-19) outbreak in Wuhan, China, Saudi Arabia started to implement several preventative measures starting with the imposition of travel restrictions to and from China. Due to the rapid spread of COVID-19, and with the first confirmed case in Saudi Arabia in March 2019, more strict measures, such as international travel restriction, and suspension or cancellation of major events, social gatherings, prayers at mosques, and sports competitions, were employed. These non-pharmaceutical interventions aim to reduce the extent of the epidemic due to the implications of international travel and mass gatherings on the increase in the number of new cases locally and globally. Since this ongoing outbreak is the first of its kind in the modern world, the impact of suspending mass gatherings on the outbreak is unknown and difficult to measure. We use a stratified SEIR epidemic model to evaluate the impact of Umrah, a global Muslim pilgrimage to Mecca, on the spread of the COVID-19 pandemic during the month of Ramadan, the peak of the Umrah season. The analyses shown in the paper provide insights into the effects of global mass gatherings such as Hajj and Umrah on the progression of the COVID-19 pandemic locally and globally.

The p-median problem selects p source locations to serve n destinations such that the average distance between the destinations and corresponding sources is minimized. It is a well-studied NP-hard combinatorial optimization problem with many existing heuristic solutions, however, existing algorithms are not scalable for large-scale problems. The fast interchange (FI) heuristic which yields results close to the optimal solution with respect to the objective function value becomes suboptimal with respect to time requirements for large-scale problems. We present a novel distributed divide and conquer algorithm, EM-FI, to solve large-scale p-median problems quickly even with limited computing resources. The algorithm identifies the existing spatial clusters of the destination locations using expectation maximization (EM) and solves them as independent p-median problems using integer programming or FI concurrently. The proposed algorithm showed an order of magnitude improvement in time without the loss of quality in terms of the objective function value on synthetic and real datasets.

The p-median problem selects p source locations to serve n destinations such that the average distance between the destinations and corresponding sources is minimized. It is a well-studied NP-hard combinatorial optimization problem with many existing heuristic solutions, however, existing algorithms are not scalable for large-scale problems. The Fast Interchange (FI) heuristic which yields results close to the optimal solution with respect to the objective function value becomes suboptimal with respect to time requirements for large-scale problems. We present a novel distributed multi-core divide and conquer algorithm, EM-FI, to solve large-scale p-median problems quickly even with limited computing resources. The algorithm identifies the existing spatial clusters of the destination locations using Expectation Maximization(EM) and solves them as independent p-median problems using Integer Programming or FI concurrently. The proposed algorithm showed an order of magnitude improvement in time without the loss of quality in terms of the objective function value on synthetic and real datasets.