[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-328307-105":59,"doc-detail-328307-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","revealing-endogenous-conditions-for-petos-paradox-via-an-ordinary-differential-equation-model","Revealing endogenous conditions for Peto’s paradox via an ordinary differential equation model","","Cancer, closely tied to cellular mutations, is often expected to rise with cell number and species lifespan, yet cancer rates across species remain remarkably uniform, a phenomenon known as Peto’s paradox. This study treats tumor progression as a multi–cell-type interaction problem and applies a Lotka-Volterra ordinary differential equation model in an immune environment. Using nondimensionalization and comparing characteristic time scales in the ODE dynamics with species cell-cycle timing, the work derives sufficient conditions that explain the observed non-correlation and clarifies why cancer incidence distributes evenly across species.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/revealing-endogenous-conditions-for-petos-paradox-via-an-ordinary-differential-equation-model/328307/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/revealing-endogenous-conditions-for-petos-paradox-via-an-ordinary-differential-equation-model/328307.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What question does the study address about Peto’s paradox?","Question",{"text":112,"@type":113},"It investigates how larger, longer-lived organisms evolve mechanisms that counteract the increased likelihood of cancer, aiming to mathematically explain the non-correlation between cancer incidence and species size or lifespan.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What modeling approach is used in this paper?",{"text":117,"@type":113},"The study employs a Lotka-Volterra ordinary differential equation model to study the evolution of cancerous cells and cancer incidence within an immune environment.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the paper explain the absence of correlation in Peto’s paradox?",{"text":121,"@type":113},"It derives sufficient conditions using nondimensionalization and by relating the ODE model’s characteristic time interval for cell population variation to the species cell-cycle time scale.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},328307,1790143668,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","Revealing endogenous conditions for Peto’s paradox via an ordinary differential equation model  \nHaichun Kan1 · Yu Chen1  \nReceived: 27 July 2023 / Revised: 21 June 2024 / Accepted: 24 June 2024 /  \nPublished online: 6 July 2024 © The Author(s) 2024  \nAbstract  \nCancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto’s paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto’s paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.  \nKeywords Peto’s paradox · Ordinary differential equation model · Nondimensionalization · Power law · Lotka-Volterra model · Cancer-immune competition  \nMathematics Subject Classification 37N25 · 92-10  \nB Yu Chen[chen@edu.k.u-tokyo.ac.jp](chen@edu.k.u-tokyo.ac.jp)  \nHaichun Kan  \n[kan.haichun@s.h.k.u-tokyo.ac.jp](kan.haichun@s.h.k.u-tokyo.ac.jp)  \n1 SCS Laboratory, Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan  \n1 Introduction  \n1.1 Background on Peto’s paradox  \nCancer continues to be a perplexing issue within the realms of biology and medicine, prompting humanity’s ongoing quest for understanding and resolution. As a disease intrinsically connected to somatic mutations, one might expect larger and longer-lived organisms to be more susceptible to cancer than their smaller and shorter-lived counterparts, given the increased number of cell divisions and the assumption that mutation rates remain constant across species during these divisions. However, this anticipated association is not observed, giving rise to the phenomenon known as “Peto’s Paradox”(Peto et al. 1975; Peto 2016) . This puzzling lack of correlation has been substantiated through a comprehensive investigation involving 191 species of zoo mammals (Vincze et al. 2021), further emphasizing the enigmatic nature of cancer incidence and its relationship with an organism’s cell count and longevity.  \n1.2 Objective of the study  \nThe intriguing question of how larger and longer-lived organisms have evolved mechanisms to counteract the increased likelihood of cancer development has piqued scientific interest, as unravelling this mystery may hold the key to advancing human cancer treatment. Prior investigations into Peto’s paradox have explored factors such as tumour suppressor genes and energy turnover rates. For example, the comparatively lower cancer rates in elephants have been attributed to their additional copies of the TP53 gene (Abegglen et al. 2015; Sulak et al. 2016) . Furthermore, Maciak and Michalak’s research (2015) posits that larger animals’ reduced energy turnover rates contribute to a decreased risk of cancer initiation. Salazar-Bañuelos’ study (2019) examined the immune system, specifically the balance between reactive and suppressive lymphocyte clones, and attempted to elucidate the paradox using a Polya’s Urn model. However, this approach yielded a negative correlation rather than the anticipated non-correlation between cancer risks and species’ cell numbers. In our current research, we aim to shift the focus from clone ratios to the interplay within the cancer-healthy-immune system triad. By examinin","cbCaikxk7Ziuj52w","https://ap.wps.com/l/cbCaikxk7Ziuj52w","pdf",2447550,29,"English","# Introduction\n## Background on Peto’s paradox\n## Objective of the study\n## Structure of the paper\n# Literature review\n## Previous research on Peto’s paradox and gaps","[{\"question\":\"What question does the study address about Peto’s paradox?\",\"answer\":\"It investigates how larger, longer-lived organisms evolve mechanisms that counteract the increased likelihood of cancer, aiming to mathematically explain the non-correlation between cancer incidence and species size or lifespan.\"},{\"question\":\"What modeling approach is used in this paper?\",\"answer\":\"The study employs a Lotka-Volterra ordinary differential equation model to study the evolution of cancerous cells and cancer incidence within an immune environment.\"},{\"question\":\"How does the paper explain the absence of correlation in Peto’s paradox?\",\"answer\":\"It derives sufficient conditions using nondimensionalization and by relating the ODE model’s characteristic time interval for cell population variation to the species cell-cycle time scale.\"}]","Revealing endogenous conditions for Peto’s paradox via an ordinary differential equation model | PDF",1789979260,73]