Environmental Persistence Influences Infection Dynamics for a Butterfly Pathogen via New Generalised Caputo Type Fractional Derivative

Abstract

In this article, we studied the outcomes of environmental transmission for infection dynamics of a debilitating protozoan parasite (Ophryocystis elektroscirrha) that infects monarch butterflies (Danaus plexippus) via new generalised Caputo type fractional derivatives. We solved a non-linear fractional model by using modified version of well known Predictor-Corrector scheme. Existence and uniqueness analysis of the given problem are exemplified by the help of important results. We gave all necessary and sufficient graphical analysis to show the nature of the given ecological model at various non-integer order values. The proposed fractional dynamical model better explores environmental persistence for this host pathogen system. We explored the graphical simulations at different shedding rate of infectious doses onto leaves and different decay rate of infectious doses on milkweed leaves. The novelty of this work is to better explore the dynamics of the model and role of the given parameters at different numerical values. Also this model is yet not solved via any fractional derivatives which can be confirmed from literature. So this fresh non-integer order model makes this study more visible to the literature. By the help of our simulations we show the beauty of fractional derivatives in the ecology. The present study is effective and interesting in the view of applications of fractional derivatives in ecological studies. (c) 2021 Elsevier Ltd. All rights reserved.