Presentation Information
[POS-17]Mathematical analysis of the point pattern SIRI model
*Kaho Toramatsu1 (1. Graduate School of Humanities and Sciences, Nara Women's University (Japan))
Keywords:
Individual-Based Model,Singlet and pair dynamics
In recent years, the number of patients with alcoholism, drug addiction, gambling, and other addictions has been on the rise. It is important to clarify the mechanisms of their transmission in order to control their increase and to promote their reintegration into society. The SIRI model, which adds reinfection to the classical SIR model, has been used to solve the dynamics of dependent patients such as drug addiction. In the SIRI model given by ODE, however, spatial structure is neglected. In this study, we extend the ODE model to a spatial population dynamics in terms of "point pattern approach". In addition to simulation analysis, we derive an analytical model that focuses on singlet and pair probabilities, and compare with simulation results.
Each individual as a point has (x, y) coordinate and a status that changes stochastically from S to I to R back to I. We assume that infection and reinfection rates depend on distanced and that recovery occurs at a constant. Infection and reinfection occur with the range σSI and σRI. Our model is an individual-based model. The number of points as the first-order structure and the pair correlation function (pair distance distribution consisting of two points) as the second-order structure are used to quantify the point pattern dynamics. In addition, the analytical model is a coupled differential equation model expressed in terms of singlet and pair probabilities.
Main results are as follows: For the first-order structure, point pattern SIRI model behaves qualitatively the same way as ODE SIRI model. With respect to the second-order structure, I-R pairs show anti-clustered distributions at equilibrium. On the other hand, R-R pairs show anti-cluster distribution for σSI >σRI is supported by the analytical model. The observed anti-clustered distribution of I–R pairs may be attributed to the reinfection of R individuals in the vicinity of I individuals, causing them to revert to the I state.In future study, we need to focus on how the results are affected under more general situations, such as those involving movement of point, and their births, and deaths.
Each individual as a point has (x, y) coordinate and a status that changes stochastically from S to I to R back to I. We assume that infection and reinfection rates depend on distanced and that recovery occurs at a constant. Infection and reinfection occur with the range σSI and σRI. Our model is an individual-based model. The number of points as the first-order structure and the pair correlation function (pair distance distribution consisting of two points) as the second-order structure are used to quantify the point pattern dynamics. In addition, the analytical model is a coupled differential equation model expressed in terms of singlet and pair probabilities.
Main results are as follows: For the first-order structure, point pattern SIRI model behaves qualitatively the same way as ODE SIRI model. With respect to the second-order structure, I-R pairs show anti-clustered distributions at equilibrium. On the other hand, R-R pairs show anti-cluster distribution for σSI >σRI is supported by the analytical model. The observed anti-clustered distribution of I–R pairs may be attributed to the reinfection of R individuals in the vicinity of I individuals, causing them to revert to the I state.In future study, we need to focus on how the results are affected under more general situations, such as those involving movement of point, and their births, and deaths.