Abstract
In this paper, a stochastic SICA epidemic model with standard incidence rate for HIV transmission is proposed. The sufficient conditions of the extinction and persistence in mean for the disease are established. Numerical simulations show that random perturbations can suppress disease outbreaks and the risk of HIV transmission can be reduced by reducing the transmission coefficient of HIV while increasing the strength of the stochastic perturbation.
Highlights
To the best of our knowledge, the human immunodeficiency virus (HIV) is a retrovirus that causes HIV infection and, over time, acquired immunodeficiency syndrome (AIDS)
We choose γ = 0.07, ω = 0.9, and σ = 0.8, 1, 1.2, 1.4, and other parameter values given by Table 1 to study the impact of σ on the dynamics for the stochastic differential equation (SDE) SICA model (1.2)
We fix σ = 0.8 and choose β = 0.2, 0.4, 0.6, 0.8, 1, 1.2 and other parameters taken as in Table 1 to study the impact of β on the dynamics for the SDE SICA model (1.2)
Summary
To the best of our knowledge, the human immunodeficiency virus (HIV) is a retrovirus that causes HIV infection and, over time, acquired immunodeficiency syndrome (AIDS). In [3], the authors consider a nonlinear fractional order epidemic model for HIV transmission and analyze by including an extra compartment, namely the exposed class, to the basic SIR epidemic model They show through numerical simulations that the control measures effectively increase the quality. SIS epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals I(t). Our aim is to introduce random white noise in the environment into the deterministic model and to study the effect of random disturbance on the number of HIV.
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