Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage

Simple Summary African swine fever, as an acute, contact-transmitted infection, has a very high mortality and infectivity, and there are no effective drugs that can treat the disease. Therefore, it is necessary to take biosecurity measures in time at the beginning of the disease outbreak. In this article, media coverage is introduced into the African swine fever model, and the results indicate that real-time media coverage of the African swine fever epidemic is beneficial for breeders to scientifically prevent the spread of the epidemic in a timely manner. Through the evaluation of specific prevention and control measures, we suggest that timely disinfection and sterilization measures taken by breeding personnel after receiving relevant reports of the swine fever epidemic can effectively control the spread of the disease. African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin's maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.