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The effect of a generalized nonlinear incidence rate on the stochastic SIS epidemic model
Author(s) -
Lahrouz Aadil,
Settati Adel,
El Fatini Mohamed,
Tridane Abdessamad
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6765
Subject(s) - mathematics , epidemic model , white noise , nonlinear system , transmission (telecommunications) , incidence (geometry) , transmission rate , statistics , demography , population , geometry , physics , quantum mechanics , sociology , electrical engineering , engineering
In this paper, we aim to analyze the classical SIS epidemic model with a generalized force of infection (including nonmonotonic cases), where the transmission rate is perturbed by white noise. Using Feller's test for explosions, we prove that the disease dies out with probability one without any restriction on the model parameters.