Katia Vogt-Geisse, Calistus N. Ngonghala, Zhilan Feng

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A deterministic model for the effects on disease prevalence of the most advanced pre-erythrocytic vaccine against malaria is proposed and studied. The model includes two vaccinated classes that correspond to initially vaccinated and booster dose vaccinated individuals. These two classes are structured by time-since-initial-vaccination (vaccine-age). This structure is a novelty for vector-host models; it allows us to explore the effects of parameters that describe timed and delayed delivery of a booster dose, and immunity waning on disease prevalence. Incorporating two vaccinated classes can predict more accurately threshold vaccination coverages for disease eradication under multi-dose vaccination programs. We derive a vaccine-age-structured control reproduction number R and establish conditions for the existence and stability of equilibria to the system. The model is bistable when R < 1. In particular, it exhibits a backward (sub-critical) bifurcation, indicating that R = 1 is no longer the threshold value for disease eradication. Thus, to achieve eradication we must identify and implement control measures that will reduce R to a value smaller than unity. Therefore, it is crucial to be cautious when using R to guide public health policy, although it remains a key quantity for decision making. Our results show that if the booster vaccine dose is administered with delay, individuals may not acquire its full protective effect, and that incorporating waning efficacy into the system improves the accuracy of the model outcomes. This study suggests that it is critical to follow vaccination schedules closely, and anticipate the consequences of delays in those schedules.

Original languageEnglish
Pages (from-to)475-513
Number of pages39
JournalJournal of Biological Systems
Issue number2
StatePublished - 1 Jun 2020
Externally publishedYes


  • Backward Bifurcation
  • Control Reproduction Number
  • Partial Differential Equations
  • Vaccination Model
  • Vaccine-age Structure
  • Vector-borne Disease


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