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Optimal control and cost-effectiveness analysis of alcohol addiction and poverty dynamics in a population |
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PP: 757-776 |
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doi:10.18576/isl/130403
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Author(s) |
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J. O. Akanni,
A. A. Ayoade,
D. Enegesele,
C. E. Madubueze,
F. Fatmawati,
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Abstract |
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| Poverty and alcoholism are among the top challenges confronting societies worldwide and essential research subjects in the last few decades. This paper developed a deterministic model governed by a system of nonlinear differential equations to proffer a solution to the burden of poverty and alcoholism in a population. The model was studied under two different systems, namely: autonomous and non-autonomous systems. Under the autonomous system, the following analysis was carried out; Poverty and alcoholism reproduction number using the next-generation method; this was done to know all the parameters contributing to the dynamics of poverty and alcoholism in a population. Also, local and global sensitivity analysis was done using the normalized forward method and Latin hypercube sampling and partial rank correlation coefficients, respectively; this was done to identify the parameters of the model that most influence thy dynamical behaviour of the model. The non-autonomous model with three time-dependent controls was analyzed using Pontryagin’s Maximum Principle to find the optimal solution to the poverty and alcoholism control problem. Cost-effectiveness analysis was conducted to further affirm the results of the optimal control problem by using the average cost-effectiveness ratio and incremental cost-effectiveness ratio methods. Numerical simulations were presented to buttress all the theoretical results.
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