# How do recurrent malaria infections occur in clinical cohorts: a mathematical modelling study to support study planning

## TL;DR

This study uses mathematical models to understand how malaria infections recur in a cohort, helping researchers plan studies and estimate sample sizes.

## Contribution

The study introduces mathematical models to simulate malaria recurrence under various transmission scenarios, aiding in study design.

## Key findings

- Models with treatment and immunity (Model B) reduced recurrent infections compared to constant risk (Model A).
- Vaccination (Model C) significantly lowered both first and recurring infections.
- Seasonal variation (Model E) caused strong fluctuations in infection timing.

## Abstract

Recurrent events of infectious diseases are common and the subject of analyses in many clinical studies. A proper understanding of disease occurrence over time within a cohort provides a basis for study planning and sample size estimation. This study mathematically describes the recurrence of malaria in a malaria-naïve cohort and highlights the necessary assumptions to inform study planning.

To represent different disease transmission scenarios, five mathematical models with different levels of complexity were constructed to mimic possible real-life scenarios. Model A represents the simplest model with constant infection risk, Model B includes protection due to treatment and reduced individual susceptibility after each infection, Model C shows preventive effects from a vaccination, Model D explores heterogeneous transmission with varying levels of infection risks, and Model E captures temporal dynamics through seasonal variation in infection risk. The models were implemented as compartmental models using a system of ordinary differential equations.

The different transmission scenarios strongly affected the pattern of recurrent infections. Models A and B had the same number of cases with infections; however, due to treatment effects and immunity development, the number of recurrent events was lower in Model B. Compared to Model B, Model C showed a substantial reduction in both first and recurring infections. In Model D, the subpopulation with a high transmission risk had a higher proportion of recurrent infections, with nearly 100% of this group experiencing more than one infection. Model E demonstrated how seasonal transmission risk leads to temporal dynamics with strong fluctuations in the occurrence of infections. Based on these models, we provide examples of how final cohort sizes can be estimated for different transmission settings.

Recurrent infections in longitudinal studies cannot be estimated directly from disease frequency data. However, this study provides a simple set of equations to calculate the number of expected recurrent events. These models can be easily adapted to represent additional transmission and infection dynamics or to model other recurrent diseases like influenza.

The online version contains supplementary material available at 10.1186/s12936-025-05594-1.