Optimal cost-effectiveness analysis of a mathematical model of climate change induced by excessive emission of carbon dioxide

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.