Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness

In this work, we study a mathematical model describing the dynamics of the transmission of African Swine Fever Virus (ASFV) between pigs on the one hand and ticks on the other hand. The aim is to Protecting pigs against the African swine fever virus. We analysis the mathematical model by using Routh–Hurwitz criteria, the local stability of ASFV-free equilibrium and ASFV equilibrium are obtained. We also study the sensitivity analysis of the model parameters to know the parameters that have a high impact on the reproduction number $R_0$. The aims of this paper is to reduce the number of infected pigs and ticks. By proposing several strategies, including the iron fencing to isolate uninfected pigs, spraying pesticides to fight ticks that transmit the virus, and getting rid of the infected and suspected pigs. Pontryagin's maximal principle is used to describe the optimal controls and the optimal system is resolved in an iterative manner. Numerical simulations are performed using Matlab. The increased cost-effectiveness ratio was computed to investigate the cost effectiveness of all possible combinations of the three controls measures. Using a cost-effectiveness analysis, we showed that controlling the protection of susceptible pigs, to prevent contact between infected pigs and infected ticks on one hand and susceptible pigs on the other hand, it is the most cost-effective strategy for disease control.