Dynamical properties of two-diffusion SIR epidemic model with Markovian switching

Abstract

Infectious diseases still remain one of the major causes of death worldwide, despite the fact that various treatments, such as antibiotics, antiviral drugs, and vaccines for some diseases, are more available to people. Factors such as drug resistance, lack of access to health care, and environmental changes contribute to their persistence and spread. Motivated by this fact, in this study, the stochastic susceptible-infectious-recovered (SIR) epidemiological model with treatment and non-linear incidence rate is extended, by introducing coloured noise, to model which takes into account the seasonal nature of the disease, as well as the fact that the disease is constantly changing through mutations, which leads to the appearance of new disease strains. For the model formulated in this way, we first prove the existence and uniqueness of the global positive solution. Then, we provide conditions under which the disease persists in the population, as well as sufficient conditions for the disease to die out. The theoretical results of the current study are validated by numerical simulations. For that purpose, we use data on the spread of the Ebola epidemic in Sierra Leone and the coronavirus disease 2019 (COVID-19) pandemic in Pakistan. Both theoretical and numerical results can lead us to conclusion that our model represents the solid research base for further investigation in the field of epidemiological modelling.

Keywords

• existence and uniqueness
• extinction
• markov chain
• persistence in mean
• sir model
• stochastic trajectories
• 60h10
• 92d25
• 93e15