Uses of the skew-logistic function for multi-wave functions

The Skew-Logistic (SL) function has been proposed to model a real-life dynamic process which rises monotonically to a peak followed by a monotonic decline. It was introduced to model the first stage of the Covid-19 pandemic to forecast the behaviour of Covid. Then, with different controls and variants, Covid levels rose and fell in what might be called a Multi-Wave (MW) behaviour; with the waves not necessarily the same size. This paper shows how using the SL function for one wave can be modified to model the MW situation. We apply it to two examples. One is to Covid -19, to examine its most recent behaviour. The other is to climate change, the most serious issue of our time. Ensuring that the world simply achieves carbon-equality is not enough. We have to rapidly achieve carbon-negativity to prevent bringing an end to the world as we know it. ### Competing Interest Statement The authors have declared no competing interest. ### Clinical Protocols ### Funding Statement No funding received. ### 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I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the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 and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes All data are available online.