A new mathematical model for transmitting and controlling Rat-Bite Fever using the theory of optimal control

Abstract

Rat-Bite Fever is a zoonotic transmitted bacterial disease caused by either Streptobacillus moniliformis or Spirillum minus. The disease is fatal and has high profile of human deaths worldwide. In this paper, we formulate a mathematical model of Rat-Bite Fever transmission under the assumption of rodent-to-human, rodent-to-rodent and environmental spread. We highlight the key determinants in the transmission of the disease and also determine and analyze the important mathematical structures of the model. In addition, we extended the model by introducing some control measures like contact-blocking equipment, use of disinfectants, treatment and hygiene practices. The theory of optimal control was explored to determine the necessary conditions for controlling the spread of the disease with minimum cost. Both the basic and the optimal control models are simulated and compared, and the result showed that multiple control strategy is the most plausible way of eliminating cases of Rat-Bite Fever in a community where enough resources are available. However, in a community where resources are scarce, single application of optimal treatment and use of protecting equipments are the alternative control strategies that can be adopted to effectively reduce the burden of the disease.

Keywords

• Optimal control analysis
• Control efficacy analysis
• Streptobacillus moniliformis
• Spirillum minus
• Rat-Bite Fever
• Global stability