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Exact Solution of Generalized Cooperative SIR Dynamics

Zarei, Fatemeh | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51575 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman; Ghanbarnejad, Fakhteh
  7. Abstract:
  8. Epidemics are one of the most important issues in social environments, economics systems, medicine, and other environments. In the study of the epidemics, some behaviors have been observed that are very similar to the phase transition in critical systems. For example, by changing the parameters that the epidemics process is characterized, the system’s epidemic behavior changes. Depending on the type of problem, this behavior change may be similar to continuous or discontinuous phase transitions. One of the fascinating issues that have just been taken into consideration in this area is the cooperation of two or more diseases. This means that the rate of transmission of a disease depends on whether the person has experienced a second disease. In the study of such systems through the mean field approximation, it has been observed that continuous phase transitions, and in some cases of a discontinuous phase transition can occur. Mostly, studies are numerical and considered for two diseases.In this research the problem of the distribution of diseases in the model SI, model SIS and model SIR is investigated; also, the twodisease cooperative equation in the model SIR, which has been solved previously by numerical methods, is analyzed and generalized to n disease. Breaking symmetry is applied, and the changes in the equilibrium state of the system are examined. Finally, we simulate transmission of 93 multiple diseases on the network. In this study, we showed that the phase transition which was observed in this system is of the hybrid type, which means that in addition to the jump in the order parameter, scale behavior is observed near the transition point. Moreover, extending it to a greater number of diseases does not change the system qualitatively, but if the symmetry is sufficiently eliminated, discontinuity in the order parameter disappears
  9. Keywords:
  10. Epidemic Spreading ; Epidemic ; Cooperative Cionfections ; Mean Field Approximation ; Breaking Time Symmetry ; Modeling ; Hybrid Phase Transition ; Susceptible Infected (SI) ; Susceptible Infected Susceptible (SIS) ; Susceptible Infected Recovered (SIR)