Optimal Control for Resource Allocation in a Multi-Patch Epidemic Model with Human Dispersal Behavior - Adikari, A.U.S.; Jayathunga, Y. (The Indonesian Bio-Mathematical Society, 2025)
A multi-patch epidemic compartmental model with human dispersal behavior studies the spread of the disease and it sets the model to real-world situations. The mobility matrix (M) applies human dispersal behavior to the model. The optimal control theory assists in controlling the disease burden while minimizing the cost of infected individuals and implementing control measures. We formulate a multi-patch SIR model with human dispersal behavior to control and reduce communicable disease outbreaks such as COVID-19 by optimizing resource allocation in Sri Lanka. Results are represented by using the reproduction number (R0), effective reproduction number (Rt), and final epidemic size (ci). Compared to the basic reproduction number (R0), the effective reproduction number (Rt) represents the significant result in the epidemiological model incorporated with control measures. The average number of secondary cases concerning the current susceptible population is represented by Rt and the final epidemic size represents the patched-specified cost value for infected individuals. According to the results, the disease burden can be controlled by vaccination relative to social distancing.