Modeling chikungunya virus infection with Black–Karasinski process: stationary distribution, probability density function, and extinction

Incorporating stochastic processes into biological models is crucial for capturing the inherent variability and uncertainties within biological systems. This paper explores the benefits of introducing Black–Karasinski process into chikungunya virus infection modeling. By utilizing the Black–Karasinski process researchers can capture the inherent variability in biological processes and account for uncertainties. This paper highlights the advantages of Black–Karasinski processes in biological modeling. We investigate the dynamical behavior of a stochastic model for chikungunya virus infection incorporating a Black–Karasinski process. Firstly, we establish sufficient conditions for the existence of a stationary distribution in the model. By solving the corresponding Fokker–Planck equation we obtain the local probability density function near the quasi-endemic equilibrium, which provides insights into the statistical characteristics of the stochastic system. Additionally, we present sufficient conditions for the extinction of infected host cells and chikungunya virus particles. Finally, we supplement the analytical results with numerical simulations to investigate the impact of random noise.