Abstract
The outbreak of a disease has negative effects on the economy, and economic activities affect the spread of a disease. In this paper, based on the relationship between economic activities and infectious diseases, we establish a SEIRG (susceptible-exposure-infective-recovered-economic) model. Applying the near-maximum condition of a Hamiltonian function, we provide sufficient and necessary conditions for the near optimal control problem of the SEIRG system. In addition, we obtain the optimal control function of the research system. Finally, we develop an algorithm for a near optimal control problem and use numerical simulations to illustrate the effects of vaccination and treatment.
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