Role of carrying capacity in dengue control: a mathematical model on waste management and public awareness

Dengue fever continues to be a significant global health challenge, influenced by the complex interplay of environmental and human behavioral factors. In this study, we propose a SEIR–SEI mathematical model that integrates human behavioral characteristics and the ecological carrying capacity of mosquitoes. Unlike previous studies, we link carrying capacity to the disease dynamics, where effective interventions in managing waste reduce the availability of breeding sites, directly influencing vector proliferation. The basic reproduction number R0 is calculated using the next-generation matrix method, and we discuss the stability analysis incorporating both local and global aspects, conducted using Lyapunov functions and the Hurwitz criterion. The models show that a decrease in carrying capacity simultaneously reduces the vector populations and dramatically changes the disease pattern, driving the system toward stability. Increasing public knowledge about diseases alters people’s behaviors that reduce disease transmission. By combining ecological, mathematical, and public health viewpoints, we show how environmental control should go hand in hand with other strategies for better disease control. This integrated approach helps in sustainable policy development and ensures applicability across related areas.