Solution Dynamics of Climate Finance Models for Mitigating Health and Economic Impacts of Climate-Induced Infectious Disease Outbreaks in Southern Nigeria Using a Semi-Analytical Method

Abstract

Climate change has heightened the frequency and intensity of infectious disease outbreaks in Southern Nigeria, with profound health and economic implications. Addressing these impacts requires not only epidemiological and environmental understanding but also sustainable financial modeling mechanisms that can allocate, predict, and optimize resource flows for mitigation. This paper presents a mathematical framework for developing a climate finance model that integrates epidemiological and economic variables through a system of coupled differential equations. The Differential Transform Method (DTM) is employed to obtain approximate analytical solutions to the nonlinear system, thereby enabling the formulation of dynamic financing policies under uncertain climate conditions. Basic theorems concerning the existence, uniqueness, and convergence of the proposed model are also established. The study provides a foundational basis for adaptive climate financing strategies aimed at reducing the health and economic burdens of climate-induced disease outbreaks.