A new mathematical model studying imperfect vaccination: Optimal control analysis

Jemal Mohammed-Awel, Eric Numfor, Ruijun Zhao, Suzanne Lenhart

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this study, a novel mathematical model is developed to investigate the effectiveness of imperfect human vaccination against malaria. The model is a system of ordinary differential equations (ODEs) coupled with a first-order partial differential equation (PDE) that describes transmission of malaria with time-since-vaccination structure for vaccinated humans. The existence and uniqueness of the solution to the system are established, the basic reproduction number (R0) is calculated, and model stability analysis of equilibria is performed. The optimal control problem, subject to the model system, is formulated with the optimal vaccination rate that minimizes the cost of implementing the imperfect vaccination as well as the number of infected humans. The optimality system is solved numerically, and several optimal control scenarios which effectively control the disease are presented.

Original languageEnglish (US)
Article number125132
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Aug 15 2021


  • Imperfect vaccine
  • Malaria
  • Optimal control

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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