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\begin{document}

\title{Optimal Cost-Effectiveness Analysis of a Mathematical Model of Climate
Change Induced by Excessive Emission of Carbon Dioxide}



\author[1]{Peter Urane Achimugwu}%
\author[2]{Mathew Ngugi Kinyanjui}%
\author[3]{David Mumo Malonza}%
\affil[1]{Pan African University Institute for Basic Sciences Technology and Innovation}%
\affil[2]{Jomo Kenyatta University of Agriculture and Technology College of Pure and Applied Sciences}%
\affil[3]{South Eastern Kenya University School of Science and Computing}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
The current crisis of global climate change and its consequences which
are manifested in form of different environmental disasters is
attributed to excessive emission and accumulation of greenhouse gases in
the atmosphere, key among which is carbon dioxide. Hence, remedies are
needed to mitigate against this change in climate. A mathematical model
on climate change incorporating good conservation policies,
enlightenment programmes and direct air capture technology as mitigation
measures is formulated and analysed using the concept of optimal control
theory and cost-effectiveness analysis. The objective functional is set
up to minimize both the excessive concentration of carbon dioxide in the
atmosphere and the total cost of implementation of each mitigation
measure, as the resources available to cater for the needs of the
teeming human population are limited. By formulating a Hamiltonian
function and using Pontryagin's Principle, the adjoint equations and
characterisation of the optimal units were calculated. Using the
optimality control system obtained, the numerical simulation was done in
MATLAB using the Forward Backward Sweep algorithm of the Runge-Kutta
Method. Seven different strategies of mitigation scenarios were
simulated. From the results, each of these strategies has the potency to
reduce the excessive concentration of carbon dioxide in the atmosphere.
However, the best result was obtained using the strategy that combines
all the three mitigation measures of good conservation policies,
enlightenment programmes and direct air capture technology. Despite that
this strategy (Strategy VII) appears the most desirable option to adopt,
the cost of implementation of each strategy has to be considered since
human resources are limited. Therefore, cost-effectiveness analysis
techniques (Average Cost-Effectiveness Ratio and Incremental
Cost-Effectiveness Ratio ) were used to arrive at the most cost-friendly
strategy. From the computations involving these two ratios, both
indicated good conservation policies strategy as the cheapest option to
adopt in reducing the excessive concentration of carbon dioxide in the
atmosphere.%
\end{abstract}%



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