A malaria model with controls on mass treatment and insecticide

Fatmawati, Hengki Tasman

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In this paper we derive a mathematical model for malaria transmis-sion in population. We use controls on mass treatment and insecticide to reduce the number of infected hosts and infected vectors. The model considers human, larvae and mosquito populations. The host popula- tion is assumed constant, but the larvae and vector populations vary. First, we investigated the existence and stability of equilibria of the model without control based on the basic reproduction ratio. Then, the Pontryagins maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically for several scenarios.

Original languageEnglish
Pages (from-to)3379-3391
Number of pages13
JournalApplied Mathematical Sciences
Issue number65-68
Publication statusPublished - 2013


  • Basic repro-duction ratio
  • Insecticide
  • Malaria
  • Mass treatment
  • Mathematical model
  • Optimal control
  • Stability


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