  Plasmodium vivax is one of the most geographically widespread malaria
parasites in the world due to its ability to remain dormant in the human liver
as hypnozoites and subsequently reactivate after the initial infection (i.e.
relapse infections). More than 80% of P. vivax infections are due to hypnozoite
reactivation. Mathematical modelling approaches have been widely applied to
understand P. vivax dynamics and predict the impact of intervention outcomes.
In this article, we provide a scoping review of mathematical models that
capture P. vivax transmission dynamics published between January 1988 and May
2023 to provide a comprehensive summary of the mathematical models and
techniques used to model P. vivax dynamics. We aim to assist researchers
working on P. vivax transmission and other aspects of P. vivax malaria by
highlighting best practices in currently published models and highlighting
where future model development is required. We provide an overview of the
different strategies used to incorporate the parasite's biology, use of
multiple scales (within-host and population-level), superinfection, immunity,
and treatment interventions. In most of the published literature, the rationale
for different modelling approaches was driven by the research question at hand.
Some models focus on the parasites' complicated biology, while others
incorporate simplified assumptions to avoid model complexity. Overall, the
existing literature on mathematical models for P. vivax encompasses various
aspects of the parasite's dynamics. We recommend that future research should
focus on refining how key aspects of P. vivax dynamics are modelled, including
spatial heterogeneity in exposure risk, the accumulation of hypnozoite
variation, the interaction between P. falciparum and P. vivax, acquisition of
immunity, and recovery under superinfection.
