Dynamics and optimal control of a spatial diffusion HIV/AIDS model with
ART and PrEP treatments
Abstract
In this paper, to investigate the synthetic effect of PrEP (pre-exposure
prophylaxis) and ART (antiretrovial therapy) on HIV transmission among
MSM (men who have sex with men) in heterogenous environment, an
realistic HIV epidemic model with spatial diffusion is established.
Here, HIV infectious people are divided into three immunity based
compartments, i.e., CD4+ T cell count less than 350, between 350 and
500, and more than 500, respectively. The basic reproduction number
$R_0$ is established and proved as a threshold parameter: The global
asymptotic stability of the disease-free steady state holds for
$R_0<1$, and the disease will be present if
$R_0>1$. Considering the substantial advantages of PrEP
and ART in controlling HIV transmissions among MSM, the optimal control
problem is presented for the case of positive constant diffusion
coefficients, which minimize the total population of susceptible
individual and HIV infected individual, the cost of PrEP and ART
thearpy. As an illustration of our theoretical results, we conduct
numerical simulations. We also conduct an optimal control case study
where model parameters are estimated from the demographic and
epidemiological data from China. This work suggests: (1) Spatial factors
cannot be ignored during the HIV intervention; (2)Taking the PrEP
intervention measure for HIV transmissions among MSM as early as
possible will help to improve the control efficiency and reduces its
cost; (3) Reducing the PrEP drug costs will promote the efficiency of
PrEP treatment in preventing the spread of HIV among MSM.