A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types
In the realm of dynamical systems described by deterministic differential equations used in biomathematical modeling, two types of random events influence the populations involved in the model: the first one is called environmental noise, due to factors external to the system; the second one is call...
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2024-12-01
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| author | Roberto Macrelli Margherita Carletti Vincenzo Fano |
| author_facet | Roberto Macrelli Margherita Carletti Vincenzo Fano |
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| description | In the realm of dynamical systems described by deterministic differential equations used in biomathematical modeling, two types of random events influence the populations involved in the model: the first one is called environmental noise, due to factors external to the system; the second one is called demographic noise, deriving from the inherent randomness of the modeled phenomenon. When the populations are small, only space-discrete stochastic models are capable of describing demographic noise; when the populations are large, these discrete models converge to continuous models described by stochastic ordinary differential systems, maintaining the essence of intrinsic noise. Moving forward again from a continuous stochastic framework, we get to the continuous deterministic setting described by ordinary differential equations if we assume that noise can be neglected. The inverse process has recently been explored in the literature by means of the so-called “backward technique” in a biological context, starting from a system of continuous ordinary differential equations and going “backward” to the reconstruction and numerical simulation of the underlying discrete stochastic process, that models the demographic noise intrinsic to the biological phenomenon. In this study, starting from a predictable, deterministic system, we move beyond biology and explore the effects of demographic noise in a novel model arising from the social sciences. Our field will be psychosocial, that is, the connections and processes that support social relationships between individuals. We consider a group of individuals having three personality types: altruistic, selfish, and susceptible (neutral). Applying the backward technique to this model built on ordinary differential equations, we demonstrate how demographic noise can act as a switching factor, i.e., moving backward from the deterministic continuous model to the discrete stochastic process using the same parameter values, a given equilibrium switches to a different one. This highlights the importance of addressing demographic noise when studying complex social interactions. To our knowledge, this is also the first time that the backward technique has been applied in social contexts. |
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| institution | Kabale University |
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| spelling | doaj-art-0ca26a5be3c5476398a0ec311aa6e1f82025-01-24T13:22:08ZengMDPI AGAxioms2075-16802024-12-01141910.3390/axioms14010009A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality TypesRoberto Macrelli0Margherita Carletti1Vincenzo Fano2Department of Biomolecular Sciences, University of Urbino “Carlo Bo”, Via Piazza S. Andrea, 34, 61029 Urbino, ItalyDepartment of Pure and Applied Sciences, University of Urbino “Carlo Bo”, Via Piazza della Repubblica, 13, 61029 Urbino, ItalyDepartment of Pure and Applied Sciences, University of Urbino “Carlo Bo”, Via Piazza della Repubblica, 13, 61029 Urbino, ItalyIn the realm of dynamical systems described by deterministic differential equations used in biomathematical modeling, two types of random events influence the populations involved in the model: the first one is called environmental noise, due to factors external to the system; the second one is called demographic noise, deriving from the inherent randomness of the modeled phenomenon. When the populations are small, only space-discrete stochastic models are capable of describing demographic noise; when the populations are large, these discrete models converge to continuous models described by stochastic ordinary differential systems, maintaining the essence of intrinsic noise. Moving forward again from a continuous stochastic framework, we get to the continuous deterministic setting described by ordinary differential equations if we assume that noise can be neglected. The inverse process has recently been explored in the literature by means of the so-called “backward technique” in a biological context, starting from a system of continuous ordinary differential equations and going “backward” to the reconstruction and numerical simulation of the underlying discrete stochastic process, that models the demographic noise intrinsic to the biological phenomenon. In this study, starting from a predictable, deterministic system, we move beyond biology and explore the effects of demographic noise in a novel model arising from the social sciences. Our field will be psychosocial, that is, the connections and processes that support social relationships between individuals. We consider a group of individuals having three personality types: altruistic, selfish, and susceptible (neutral). Applying the backward technique to this model built on ordinary differential equations, we demonstrate how demographic noise can act as a switching factor, i.e., moving backward from the deterministic continuous model to the discrete stochastic process using the same parameter values, a given equilibrium switches to a different one. This highlights the importance of addressing demographic noise when studying complex social interactions. To our knowledge, this is also the first time that the backward technique has been applied in social contexts.https://www.mdpi.com/2075-1680/14/1/9mathematical modelingdemographic noisebackward techniquealtruism |
| spellingShingle | Roberto Macrelli Margherita Carletti Vincenzo Fano A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types Axioms mathematical modeling demographic noise backward technique altruism |
| title | A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types |
| title_full | A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types |
| title_fullStr | A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types |
| title_full_unstemmed | A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types |
| title_short | A First Application of the Backward Technique in Social Sciences: Exploring Demographic Noise in a Model with Three Personality Types |
| title_sort | first application of the backward technique in social sciences exploring demographic noise in a model with three personality types |
| topic | mathematical modeling demographic noise backward technique altruism |
| url | https://www.mdpi.com/2075-1680/14/1/9 |
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