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Jayathunga, Y.
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Social Sciences

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Optimal Control for Resource Allocation in a Multi-Patch Epidemic Model with Human Dispersal Behavior Adikari, A.U.S.; Jayathunga, Y.
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.1

Abstract

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.
Gravity Model Approach to Model Epidemic with Human Dispersal Behaviors Dinasiri, A.S.K.; Jayathunga, Y.
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.2.5

Abstract

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal behaviors within a patch and between patches are considered. When the human dispersal behaviors within a patch are modeled, the denominator of the general gravity model becomes zero. An alternative power-based distance decay function is introduced to the gravity model to address that research gap. The parameters of the modified gravity model are estimated using a hybrid method combining ordinary least squares (OLS) and nonlinear least squares (NLS) methods (Hybrid OLS-NLS method).
Co-Authors Adikari, A.U.S. Dinasiri, A.S.K.