Effects of measures on phase transitions in two cooperative susceptible-infectious-recovered dynamics
Adib Khazaee1, Fakhteh Ghanbarnejad2
1Department of Physics, Sharif University of Technology, Tehran, Iran.
Insights
Immunization strategies can alter how two co-infections spread. High-rate vaccination can shift disease transitions from abrupt to gradual, impacting spread dynamics and thresholds.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Cooperative interactions in co-infections can lead to discontinuous transitions at lower thresholds.
- Understanding how interventions affect these transitions is crucial for public health strategies.
Purpose of the Study:
- To investigate the impact of immunization, with rates dependent on infection extent, on co-infection phase transitions.
- To analyze how vaccination strategies modify discontinuous transitions into continuous ones in coupled disease dynamics.
Main Methods:
- Utilized mean-field approximation for analyzing two coupled susceptible-infectious-recovered (SIR) dynamics.
- Employed numerical and analytical solutions to probe phase transitions across various parameter ranges.
- Introduced vaccination at fixed rates and rates proportional to the infectious compartment size.
Main Results:
- Sufficiently high vaccination rates can transform discontinuous co-infection transitions into continuous ones.
- These immunization measures increase the threshold required for disease transition.
- Heterogeneous mean-field approaches were explored to assess the robustness of findings under asymmetry.
Conclusions:
- Immunization strategies significantly influence the nature and threshold of co-infection phase transitions.
- Dynamic vaccination proportional to infection levels can effectively manage disease spread dynamics.
- The findings provide insights into optimizing public health interventions for co-occurring infectious diseases.
Abstract:
In recent studies, it has been shown that a cooperative interaction in a co-infection spread can lead to a discontinuous transition at a decreased threshold. Here, we investigate the effects of immunization with a rate proportional to the extent of the infection on phase transitions of a cooperative co-infection. We use the mean-field approximation to illustrate how measures that remove a portion of the susceptible compartment, like vaccination, with high enough rates can change discontinuous transitions in two coupled susceptible-infectious-recovered dynamics into continuous ones while increasing the threshold of transitions. First, we introduce vaccination with a fixed rate into a symmetric spread of two diseases and investigate the numerical results. Second, we set the rate of measures proportional to the size of the infectious compartment and scrutinize the dynamics. We solve the equations numerically and analytically and probe the transitions for a wide range of parameters. We also determine transition points from the analytical solutions. Third, we adopt a heterogeneous mean-field approach to include heterogeneity and asymmetry in the dynamics and see if the results corresponding to homogeneous symmetric case stand.
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