The necessity of modeling the dynamics of infectious disease spread is driven by the imperative to accurately predict epidemics and assess the efficacy of control measures, such as isolation and quarantine. Conventional compartmental SIR and SEIR models have been widely used for predicting the course of epidemics, but they have limitations due to their inability to account for dynamic isolation. Research frequently recognizes the assumptions underlying these models but rarely provides justification for their validity within the specific contexts where they are applied. In this paper, we propose a novel approach based on the concept of a working set, which we utilize as a subset of agents actively involved in social contact and potential transmission. Our adapted working set model incorporates isolation states for susceptible and infected agents, enabling dynamic adjustment of the transmission rate according to the current size of the Working Set. The incorporation of a time window parameter enables the identification of current contacts and the identification of superspreaders, an important component for the optimization of epidemiological measures. Experimental results and comparative analysis showed that, compared to the SIR and SEIR models, the adapted working set model provides a more detailed and realistic tool for analyzing the spread of infection under dynamic control measures. Our model accounts for contact heterogeneity and allows a better assessment of the impact of isolation. The presented approach integrates resource management principles from computer systems with epidemiological models, providing a flexible and realistic tool for evaluating and optimizing infectious disease control measures. In addition, a practical analysis of established models reveals fundamental modeling principles that can be adapted to different scenarios.
Citation: Aslanbek Murzakhmetov, Gaukhar Borankulova, Aigul Tungatarova, Saltanat Dulatbayeva, Nurgul Zhoranova, Zhazira Taszhurekova. Working Set: adapted model to the epidemiological context[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 2988-3004. doi: 10.3934/mbe.2025110
The necessity of modeling the dynamics of infectious disease spread is driven by the imperative to accurately predict epidemics and assess the efficacy of control measures, such as isolation and quarantine. Conventional compartmental SIR and SEIR models have been widely used for predicting the course of epidemics, but they have limitations due to their inability to account for dynamic isolation. Research frequently recognizes the assumptions underlying these models but rarely provides justification for their validity within the specific contexts where they are applied. In this paper, we propose a novel approach based on the concept of a working set, which we utilize as a subset of agents actively involved in social contact and potential transmission. Our adapted working set model incorporates isolation states for susceptible and infected agents, enabling dynamic adjustment of the transmission rate according to the current size of the Working Set. The incorporation of a time window parameter enables the identification of current contacts and the identification of superspreaders, an important component for the optimization of epidemiological measures. Experimental results and comparative analysis showed that, compared to the SIR and SEIR models, the adapted working set model provides a more detailed and realistic tool for analyzing the spread of infection under dynamic control measures. Our model accounts for contact heterogeneity and allows a better assessment of the impact of isolation. The presented approach integrates resource management principles from computer systems with epidemiological models, providing a flexible and realistic tool for evaluating and optimizing infectious disease control measures. In addition, a practical analysis of established models reveals fundamental modeling principles that can be adapted to different scenarios.
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Figures(4) / Tables(2)
Aslanbek Murzakhmetov, Gaukhar Borankulova, Aigul Tungatarova, Saltanat Dulatbayeva, Nurgul Zhoranova, Zhazira Taszhurekova. Working Set: adapted model to the epidemiological context[J]. Mathematical Biosciences and Engineering, 2025, 22(12): 2988-3004. doi: 10.3934/mbe.2025110
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