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An epidemic model highlighting humane social awareness and vector–host lifespan ratio variation

Abstract:

Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence systems are overwhelming against advanced propagation of the disease. News is becoming more effortlessly accessible through social media and mobile apps, while apparatuses for disease prevention are inclined to be more abundant and affordable. Here we study a simple host–vector model in which media-triggered social awareness and seasonality in vector breeding are taken into account. There appears a certain threshold indicating the alarming outbreak; the number of infective human individuals above which shall actuate the self-defence systems for the susceptible subpopulation. A model where the infection rate revolves in the likelihood of limited medical access, perceiving the disease as being easily curable, and overwhelming hungrier vectors is proposed. Further discoveries are made from undertaking disparate time scales in human and vector population. The resulting slow–fast system discloses notable dynamics in which solution trajectories confine to a slow manifold and the critical manifold, before finally ending up at stable equilibria. How coinciding the slow manifold with the critical manifold enhances periodic forcing is also studied. The finding on hysteresis loops gives insights into how defining an alarming outbreak critically perturbs the basic reproductive number, which later helps keep the incidence cycle on small magnitudes.