Article citationsMore>>

Kermack, W.O. and McKendrick, A.G. (1927) A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115, 700-721.
https://doi.org/10.1098/rspa.1927.0118

has been cited by the following article:

• TITLE: Optimal Control and Numerical Simulation of a SIHR Model with Nonlinear Birth and Incidence Rates

  AUTHORS: Qi Zhang

  KEYWORDS: Epidemic Model, Optimal Control, Pontryagin’s Maximum Principle, Limited Medical Resources, Numerical Simulation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.9, September 18, 2026

  ABSTRACT: This paper investigates optimal control strategies for an SIHR epidemic model with a nonlinear birth rate, a nonlinear incidence rate, and limited medical resources. Based on the original model, three control variables are introduced: transmission-suppression control, medical-resource saturation relief control, and treatment-efficiency enhancement control. An optimal control model is then formulated. The existence of an optimal control is established by applying the Fleming and Rishel theorem, and the necessary optimality conditions are derived from Pontryagin’s maximum principle. Numerical simulations show that the combined control strategy can substantially reduce the numbers of infected and hospitalized individuals as well as the saturation pressure on medical resources. The results indicate that coordinated interventions and expansion of medical capacity are important for disease prevention and control.