An extended catalytic model to assess changes in risk for multiple reinfections with SARS-CoV-2

Background The SARS-CoV-2 pandemic has illustrated that monitoring trends in multiple infections can provide insight into the biological characteristics of new variants. Following several pandemic waves, many people have already been infected and reinfected by SARS-CoV-2 and therefore methods are needed to understand the risk of multiple reinfections. Objectives In this paper, we extended an existing catalytic model designed to detect increases in the risk of reinfection by SARS-CoV-2 to detect increases in the population-level risk of multiple reinfections. Methods The catalytic model assumes the risk of reinfection is proportional to observed infections and uses a Bayesian approach to fit model parameters to the number of n th infections among individuals whose ( n − 1) th infection was observed at least 90 days before. Using a posterior draw from the fitted model parameters, a 95% projection interval of daily n th infections is calculated under the assumption of a constant n th infection hazard coefficient. An additional model parameter was introduced to consider the increased risk of reinfection detected during the Omicron wave. Validation was performed to assess the model’s ability to detect increases in the risk of third infections. Key Findings The model parameters converged when applying the model’s fitting and projection procedure to the number of observed third SARS-COV-2 infections in South Africa. No additional increase in the risk of third infection was detected after the increase detected during the Omicron wave. The validation of the third infections method showed that the model can successfully detect increases in the risk of third infections under different scenarios. Limitations Even though the extended model is intended to detect the risk of n th infections, the method was only validated for detecting increases in the risk of third infections and not for four or more infections. The method is very sensitive to low numbers of n th infections, so it might not be usable in settings with small epidemics, low coverage of testing or early in an outbreak. Conclusions The catalytic model to detect increases in the risk of reinfections was successfully extended to detect increases in the risk of n th infections and could contribute to future detection of increases in the risk of n th infections by SARS-CoV-2 or other similar pathogens. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement J.R.C.P. and C.v.S. are supported by the South African Department of Science and Innovation and the National Research Foundation. Any opinion, finding, and conclusion or recommendation expressed in this material is that of the authors, and the NRF does not accept any liability in this regard. This work was also supported by the Wellcome Trust (grant no. 221003/Z/20/Z) in collaboration with the Foreign, Commonwealth and Development Office, United Kingdom. Writing assistance was provided by Yuri Munsamy, PhD of SACEMA, South Africa. This assistance was funded by Stellenbosch University. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced and used are available online a and