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Multi-scale Analysis of Bacterial Growth Under Stress Treatments
Published on: November 28, 2019
Stability and threshold analysis of a class of epidemic models in a multi-patch environment
Linhe Zhu1, Le He2, Haoyan Sha1
1School of Mathematical Sciences, Jiangsu University, Zhenjiang, China.
None:
Spatial heterogeneity and population migration may affect transmission threshold and the asymptotic behavior of epidemic transmission near the steady state. To investigate this issue, an epidemic transmission model with nonlinear natural growth mechanism and linear migration mechanism based on multi-patch structure is established. First, we study the findings related to the equilibrium state of the system and the transmission threshold, proving the uniqueness and the existence of epidemic-free equilibrium points, the existence of positive equilibrium points under certain conditions and the non-existence of mixed equilibrium points. Meanwhile, we discuss the asymptotic behavior of various types of equilibrium points and define the global basic reproduction number and the local basic reproduction number, demonstrating some of their unequal relationships. Further, we also consider the impact of the blocking mechanism on the patch model, illustrating that the epidemic disappears or persists in single patch under certain conditions. Finally, we carry out the numerical simulation analysis of our system. The results suggest that the epidemic may form a certain oscillatory pattern in space and there are multiple positive equilibrium points for the system. At the same time, the blocking mechanism may lead to different types of equilibrium states in different patches, but it is not effective in reducing the total number of infected individuals and the convergence time of the system.
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