  Asymptomatic individuals in the context of malarial disease refers to
subjects who carry a parasite load but do not show clinical symptoms. A correct
understanding of the influence of asymptomatic individuals on transmission
dynamics will provide a comprehensive description of the complex interplay
between the definitive host (female \textit{Anopheles} mosquito), intermediate
host (human) and agent (\textit{Plasmodium} parasite). The goal of this article
is to conduct a rigorous mathematical analysis of a new compartmentalized
malaria model accounting for asymptomatic human hosts for the purpose of
calculating the basic reproductive number ($\mathcal{R}_0$), and determining
the bifurcations that might occur at the onset of disease free equilibrium. A
point of departure of this model from others appearing in literature is that
the asymptomatic compartment is decomposed into two mutually disjoint
sub-compartments by making use of the naturally acquired immunity (NAI) of the
population under consideration. After deriving the model, a qualitative
analysis is carried out to classify the stability of the equilibria of the
system. Our results show that the dynamical system is locally asymptotically
stable provided that $\mathcal{R}_0<1$. However this stability is not global,
owning to the occurrence of a sub-critical bifurcation in which additional
non-trivial sub-threshold equilibrium solutions appear in response to a
specified parameter being perturbed. To ensure that the model does not undergo
a backward bifurcation, we demand that an auxiliary parameter denoted
$\Lambda<1$ in addition to the threshold constraint $\mathcal{R}_0<1$. The
authors hope that this qualitative analysis will fill in the gaps of what is
currently known about asymptomatic malaria and aid in designing strategies that
assist the further development of malaria control and eradication efforts.
