Global stability of a multistrain SIS model with superinfection and patch structure

Abstract

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235-247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters. KEYWORDS global asymptotic stability, multigroup epidemic model, multistrain model, patch model MSC CLASSIFICATION 92D30; 34D23 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Relationship between addicts with incurable diseases in an epidemic model

“…Study of the transmission dynamics of infectious diseases with multiple strains is of great importance in mathematical epidemiology. Therefore, epidemic models with multiple strains such as HIV, malaria, … , introduced in previous movies, [1][2][3][4][5][6][7][8] have been attracted considerable attention.…”

“…Super infection introduced in previous studies. 3,[9][10][11] Unfortunately, heroin is one of the most widely used drugs in the word. White and Comiskey have introduced the first model for the dynamics of heroin users, 12 by using the following system of equations:…”