Multi-objective optimization and nonlinear dynamics for sub-healthy COVID-19 epidemic model subject to self-diffusion and cross-diffusion

The spread of infectious diseases in COVID-19 is influenced by many factors, such as the physical condition of susceptible individuals, medical level, vaccination, individual diffusion, and the conscious avoidance behavior of susceptible populations towards infected individuals. Based on these factors, this paper proposes a sub-health COVID-19 model with self-diffusion and cross-diffusion. First, we prove the system’s basic properties and perform the endemic equilibrium’s asymptotic distribution under minor diffusion conditions. Then, we construct the optimal control system based on regional control, mask-wearing and medical treatment, and obtain the optimal control solution. Next, the global sensitivity is analyzed to determine the parameters’ sensitivity. Moreover, we implement multi-objective optimization analysis based on social costs C(θ3,δ), social benefits B(θ3,δ) and threshold R0(θ3,δ). The Pareto front gives maximum social cost MSC=3×105 and maximum social benefit MSB=1×106. Meantime, we provide the COVID-19 control’s optimal path OQ⃗=(θ3⋆,δ⋆) based on medical treatment and vaccination protection. Finally, how factors such as self-diffusion, cross-diffusion, sub-healthy population and outbreak area’s number affect the disease’s spatial spread is numerically illustrated. Our results indicate: (1) The greater the self-diffusion, the faster the disease will spread. However, the larger the chemotactic coefficient, the slower the disease will spread. Even a large chemotactic coefficient will lead to the disease’s disappearance. (2) Excessive proportion of sub-healthy people is not conducive to disease control and will increase the difficulty of disease control. (3) Multi-area outbreaks spread faster and have a larger disease scale than single-area outbreaks.