Gravity Model Approach to Model Epidemic with Human Dispersal Behaviors

A.S.K. Dinasiri; Y. Jayathunga

doi:10.5614/cbms.2024.7.2.5

Authors

A.S.K. Dinasiri Department of Mathematics, Faculty of Science, University of Colombo, Colombo 03, Sri Lanka
Y. Jayathunga Department of Mathematics, Faculty of Science, University of Colombo, Colombo 03, Sri Lanka

DOI:

https://doi.org/10.5614/cbms.2024.7.2.5

Keywords:

Gravity model with human dispersal behaviors, distance decay function, multi-patch compartmental model, OLS, NLS, hybrid OLS-NLS method

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).

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