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Competing Interests: Declaration of interests Thirteen of the authors (ZA, S-CH, LJ, AM, CO, MO, JP, YP-S, DS, LB-V, MRo, MW, and HW) were compensated for their time while drafting and developing the Lancet Countdown's report. LC was supported by a grant from the National Heart, Lung, and Blood Institute of the National Institutes of Health. CD received funding from the European Research Council (FLORA, grant number 101039402). RD was supported by a grant from the High Tide Foundation and subcontracts on funds from the Wellcome Trust and US Centers for Disease Control and Prevention. GG-S received funding from the UK National Institute for Health and Care Research for the Global Health Research Group on Diet and Activity (NIHR133205, with sub-award contract number G109900-SJ1/171 with the University of Cambridge). SHG's research was supported by the National Research Foundation, Prime Minister's Office, Singapore, under its Campus for Research Excellence and Technological Enterprise programme (grant number NRF2019-THE001-0006). JJH was supported by two grants from the Wellcome Trust and a grant from the US National Science Foundation. RH, RK, and MSo acknowledge funding from Academy of Finland projects HEATCOST (grant 334798) and VFSP-WASE (grant 359421), together with EU Horizon projects FirEUrisk (grant number 101003890) and EXHAUSTION (grant number 820655). OJ was supported by grants from the National Health Medical Research Council (Heat and Health: building resilience to extreme heat in a warming world, GNT1147789); Wellcome Trust (Heat stress in ready-made garment factories in Bangladesh and the Heat inform pregnant study); and Resilience New South Wales (A new heat stress scale for general public); holds a patent for the Environmental Measurement Unit; and has received consulting fees from the National Institutes of Health. HM received funding from the Oak Foundation to support work on climate change through RealZero, is partly funded by the National Institute for Health Research's Comprehensive Biomedical Research Centre at University College London Hospitals, and received fees from Bayer Pharmaceuticals and Chiesl for sustainability consulting. JM-U was supported by grants PID2021-127107NB-I00 from Ministerio de Ciencia e Innovación (Spain) and 2021 SGR 00526 from Generalitat de Catalunya (Spain). JRo's work is supported by the Alexander von Humboldt foundation. RL, JRo, and MRo were supported by Horizon Europe through the IDAlert project (101057554) and UK Research and Innovation (reference number 10056533). RNS reports a contract with Massachusetts General Hospital. MSo and AU were supported by the Finnish Foreign Ministry project IBA-ILMA (grant number VN/13798/2023). MSp was supported by funding from the Wellcome Trust, through Our Planet Our Health (Livestock, Environment and People, award number 205212/Z/16/Z) and a Wellcome Career Development Award (Towards the full cost of diets, award number 225318/Z/22/Z). JDSh was supported by the Canadian Institutes of Health Research, the Commonwealth Fund, and the Emergency Care Research Institute and has received consulting fees from the Institute for Healthcare Research. JT was supported by the Research Council of Finland (T-Winning Spaces 2035 project), the UK Medical Research Council (PICNIC project), and the Finnish Ministry of the Environment (SEASON project). JB is employed as a consultant by the Global Climate and Health Alliance. ML received consulting fees from YarCom for advisory services and was supported by general use gifts awarded to the Center on Global Energy Policy at Columbia University, USA. JMil acknowledges consulting fees from the C40 Climate Leadership Group. CZ-C received a consultancy from the University of Alberta and was supported by contracts with her university (Universidad Peruana Cayetano Heredia), University of Leeds, WHO, and the Wellcome Trust; she was also supported by a letter of agreement between her university and the Food and Agriculture Organization's Indigenous Peoples Unit. MD was supported by the Wellcome Trust via the Complex Urban Systems for Sustainability and Health project (grants 205207/Z/16/Z and 209387/Z/17/Z). IH, S-CH, MRo, CT, and RL were supported by the Horizon Europe CATALYSE project (CATALYSE grant number 101057131, HORIZON-HLTH-2021-ENVHLTH-02, with UK Research and Innovation reference number 10041512). The work of YH, YL, DT, and QZ was supported by the National Aeronautics and Space Administration's Earth Action programme (grant number 80NSSC21K0507). AJP was supported by the Bezos Earth Fund and the Schmidt Family Foundation. ER and SD were supported by a Process-based models for climate impact attribution across sectors (PROCLIAS) grant (COST Action PROCLIAS grant CA19139), funded by European Cooperation in Science and Technology. All other authors declare no competing interests.

Diagnostic testing followed by isolation of identified cases with subsequent tracing and quarantine of close contacts-often referred to as test-trace-isolate-and-quarantine (TTIQ) strategy-is one of the cornerstone measures of infectious disease control. The COVID-19 pandemic has highlighted that an appropriate response to outbreaks of infectious diseases requires a firm understanding of the effectiveness of such containment strategies. To this end, mathematical models provide a promising tool. In this work, we present a delay differential equation model of TTIQ interventions for infectious disease control. Our model incorporates the assumption of limited TTIQ capacities, providing insights into the reduced effectiveness of testing and tracing in high prevalence scenarios. In addition, we account for potential transmission during the early phase of an infection, including presymptomatic transmission, which may be particularly adverse to a TTIQ based control. Our numerical experiments inspired by the early spread of COVID-19 in Germany demonstrate the effectiveness of TTIQ in a scenario where immunity within the population is low and pharmaceutical interventions are absent, which is representative of a typical situation during the (re-)emergence of infectious diseases for which therapeutic drugs or vaccines are not yet available. Stability and sensitivity analyses reveal both disease-dependent and disease-independent factors that impede or enhance the success of TTIQ. Studying the diminishing impact of TTIQ along simulations of an epidemic wave, we highlight consequences for intervention strategies., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Heidecke et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Competing Interests: Declaration of interests 14 of the authors (MRo, MWa, LJ, MBO'H, CO, HW, CdN, HK, PL, DS, CG, ZA, MY-G, and KRvD) were compensated for their time while drafting and developing the Lancet Countdown's report. OG was supported by the EU Horizon Grant: Climate Action To Advance Healthy Societies in Europe (Project 101057131–CATALYSE), for which there is overlap of data collection and preprocessing with the materials submitted in this report. MSp was supported by the Wellcome Trust Livestock, Environment and People (grant number 205212/Z/16/Z) and Wellcome Trust (grant number 225318/Z/22/Z). JT was supported by the Academy of Finland grants for the T-Winning (grant number 353327). CD was supported by the UK Natural Environment Research Council Independent Research Fellowship (grant number NE/N01524X/1), which ended in 2021, and by the European Research Council starting grant FLORA (grant number 101039402). OJ was supported by the NHMRC Investigator Grant entitled Heat and Health: Building resilience to extreme heat in a warming world (GNT20009507), the Wellcome Trust grant Heat stress in ready-made garment factories in Bangladesh (216059/Z/19/Z), and the Resilience New South Wales grant A new heat stress scale for general public (PJ-0000850). YL was supported by funding from the National Aeronautics and Space Administration (grant number: 80NSSC21K0507) for the wildfire population exposure and fire danger indicators. TO and IH were supported by the UK Research and Innovation Engineering and Physical Sciences Research Council Centre for Research in Energy Demand Solutions (grant number EP/R035288/1). MRo was supported by funding from IDAlert project (UK Research and Innovation project reference number 10056533). KB was supported by funding from the National Institute for Health and Care Research (NIHR) Centre on Non-communicable Diseases and Environmental Change (NIHR203247). All other authors declare no competing interests. The authors alone are responsible for the views expressed in this Commission, and they do not necessarily represent the views, decisions, or policies of the institutions with which they are affiliated.