Trade-offs between chemotaxis and proliferation shape the phenotypic structuring of invading waves

Chemotaxis-driven invasions have been proposed across a broad spectrum of biological processes, from cancer to ecology. The influential system equations introduced by Keller and Segel has proven popular choice in the modelling such phenomena, but its original form restricts homogeneous population. To account for possibility phenotypic heterogeneity, we extend case population continuously structured space, time phenotype, where latter determines variation chemotactic responsiveness, proliferation rate, level chemical environment modulation. extended model considered here comprises non-local partial differential equation local phenotype distribution cells which is coupled, through an integral term, with concentration attractant, sensed degraded cells. In framework this model, concentrate on chemotaxis/proliferation trade-off scenario, cell phenotypes span states highly-chemotactic minimally-proliferative minimally-chemotactic highly-proliferative. Using combination numerical simulation formal asymptotic analysis, explore properties travelling-wave solutions. results our study demonstrate how incorporating heterogeneity may lead highly-structured wave profile, different dominate spatial positions invading wave, clarify structuring can be shaped trade-offs between chemotaxis proliferation.