Abstract
A two-patch epidemic model is considered in order to assess the impact of virtual dispersal on disease transmission dynamics. The two-patch system models the movement of individuals between the two-patches using a residence-time matrix P, where P depends on both residence times and state variables (infected classes). In this work, we employ this approach to a general two-patch SIR model in order to investigate the effect of state dependent dispersal behaviors on the disease dynamics. Furthermore, optimal control theory is employed to identify and evaluate patch-specific control measures aimed at reducing disease prevalence at a minimal cost. Optimal policies are computed under various dispersal scenarios (depending on the different residence-time matrix configurations). Our results suggest there is a reduction of the outbreak and the proportion of time spent by individuals in a patch exhibits less fluctuations in the presence of patch-specific optimal controls. Furthermore, the optimal strategies for each patch differ depending on the type of dispersal behavior and the different infection rate in a patch. In all of our results, we obtain that the optimal strategies reduce the number of infections per patch.
Highlights
Modeling the transmission of diseases has been studied over the past decades in a variety of forms, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
Real-world examples of public health concerns included the potential threat of the spread of the Zika virus following the Rio 2016 Olympics in Brazil, when thousands of humans worldwide traveled to Brazil and returned to their home countries [18]
We present an optimal control formulation for two-patch SIR models under virtual dispersal where the control function represents interventions or policy for personal protection
Summary
Modeling the transmission of diseases has been studied over the past decades in a variety of forms, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. COVID-19 has resulted in 1,689,724,318 confirmed cases and 663,470 fatalities as of 30 July 2020 and its impact ranged from countries’ public health systems to their economies This scenario raises a general question about the potential worldwide spread of diseases, as humans and other living organisms are no longer restricted by man-made and natural boundaries. In [16], optimal strategies for two-patch dengue transmission is numerically studied via optimal control problems As this is a theoretical model where we approximate solutions computationally, we refer to the travel of populations between two locations, as virtual dispersal in the Lagrangian framework based on [15].
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