Bifurcation Analysis of an Age Structured Malaria Model

Abstract

Malaria is one of the diseases that account for the highest mortality in sub-Saharan Africa
particularly among children below the age of five. On 17 April 2023, Nigeria became the
second country in the world to approve R21 malaria vaccine to prevent malaria infections
in children from five months to thirty-six months of age. In an attempt to investigate the
implications of vaccine development for malaria and the subsequent approval of its use in some
endemic regions, an age-structured malaria model was designed and some important factors
that could shape malaria dynamics were incorporated (e.g. vaccination, nonlinear incidence,
asymptomatic carriers, relapse and migration). The validity of the model is established using
some mathematics theorems and the reproduction number is computed following the next
generation matrix method. Bifurcation analysis is conducted by employing the center manifold
theorem. The results of the study indicated that the development of malaria vaccines and
the subsequent approval of its use in some malaria endemic regions (e.g. Ghana, Nigeria,
etc.) are a welcome development. However, while the vaccines may guarantee the necessary
protection, its application and coverage to the fullest may not instigate malaria eradication.
The policy implication of the results is that the prevalence of vectors in the endemic regions
necessitated adequate vector control in addition to the application of vaccines to minimize
malaria transmission.