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

(2025) 24:329 Krumkamp et al. Malaria Journal https://doi.org/10.1186/s12936-025-05594-1 Malaria Journal Open Access RESEARCH How do recurrent malaria infections occur in clinical cohorts: a mathematical modelling study to support study planning Ralf Krumkamp1,2*, Lydia Helen Rautman1,2, Oumou Maiga‑Ascofaré1,2,3, Jürgen May1,2,4 and Eva Lorenz1,2 Abstract Background 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. Methods To represent different disease transmission scenarios, five mathematical models with different lev‑ els 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 trans‑ mission 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. Results 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 reduc‑ tion 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. Conclusions 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 recur‑ rent diseases like influenza. Keywords Cohort studies, Sample size, Mathematical modelling, Malaria, Recurrent infection *Correspondence: Ralf Krumkamp Full list of author information is available at the end of the article © The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Krumkamp et al. Malaria Journal (2025) 24:329 Background In many longitudinal cohort studies, single events per person, like time to disease onset or death, are analysed and survival analysis is used to study intervention effects. For this kind of data Kaplan–Meier methods to estimate the survival function and Cox proportional hazard models to estimate the hazard ratio are common analytical methods [1]. However, several diseases cause outcomes that can recur within one patient. Epileptic seizures, asthma attacks or cardiac arrythmia are examples of non-communicable diseases that may recur. Recurrent events are also common in communicable diseases. Infectious diseases with short recovery times and partial or fast-waning immunity can cause several episodes per person. Examples include clinical malaria episodes due to Plasmodium falciparum parasite infection and influenza infections during endemic seasons. Recurrent disease episodes in longitudinal studies are of clinical interest as they provide information about a patient’s prognosis, individual susceptibility or differences in infection risk. For example, in malaria vaccine efficacy trials (phase III), the time to first disease episode after the primary series of vaccinations is often the main endpoint. However, the efficacy of a vaccine against recurrent infections is also reported [2, 3]. Various methods have been proposed for analysing the effects of interventions on data from recurrent events in longitudinal studies, such as extensions of the Cox model (Andersen-Gill, Prentice-WilliamsPeterson, Wei-Lin-Weissfeld models) and frailty models [4]. Sample size formulas for the analyses of recurrent events have been developed and are well described [5–9]. These calculations determine the number of participants needed in an intervention and control group to estimate an effect with a desired level of precision. Limited methodological guidance exists about how recurrent disease episodes are represented in longitudinal studies. However, a proper understanding is relevant for study planning and conduct; for example, to make assumptions for sample size estimation or predict recurrent disease patterns in a cohort to plan follow-up procedures. It is important to note that the occurrence of recurrent infections cannot be predicted from disease frequency data directly. Recurrence is a temporal process in which individuals transition towards states of experiencing successive disease events [10]. This study aims to demonstrate the dynamics of disease recurrence in population cohorts and is structured as follows: (1) introduction of a mathematical framework for modelling recurrent malaria infections, (2) application of these models to explore different patterns of disease recurrence using real-life scenarios, and (3) use of the models to estimate the number of cases and events in longitudinal studies. Although malaria is used as an example, the Page 2 of 11 principles and methods presented here can be applied to other, also non-communicable conditions with recurrent outcomes. Methods A common estimator for the frequency of disease in a population at risk is the incidence proportion (IP), also called cumulative incidence. The IP ranges from 0 to 100%, and shows the individual risk to experie (...truncated)