Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients
Discarded plastic is subjected to weather effects from different ecosystems and becomes microplastic particles. Due to their small size, they have spread across the planet. Their presence in living organisms can have several harmful consequences, such as altering the interaction between prey and pre...
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MDPI AG
2022-08-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/27/4/66 |
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| author | Lindomar Soares Dos Santos José Renato Alcarás Lucas Murilo Da Costa Mateus Mendonça Ramos Simões Alexandre Souto Martinez |
| author_facet | Lindomar Soares Dos Santos José Renato Alcarás Lucas Murilo Da Costa Mateus Mendonça Ramos Simões Alexandre Souto Martinez |
| author_sort | Lindomar Soares Dos Santos |
| collection | DOAJ |
| description | Discarded plastic is subjected to weather effects from different ecosystems and becomes microplastic particles. Due to their small size, they have spread across the planet. Their presence in living organisms can have several harmful consequences, such as altering the interaction between prey and predator. Huang et al. successfully modeled this system presenting numerical results of ecological relevance. Here, we have rewritten their equations and solved a set of them analytically, confirming that microplastic particles accumulate faster in predators than in prey and calculating the time values from which it happens. Using these analytical solutions, we have retrieved the Lotka–Volterra predator–prey model with time-varying intraspecific coefficients, allowing us to interpret ecological quantities referring to microplastics dispersion. After validating our equations, we solved analytically particular situations of ecological interest, characterized by extreme effects on predatory performance, and proposed a second-order differential equation as a possible next step to address this model. Our results open space for further refinement in the study of predator–prey models under the effects of microplastic particles, either exploring the second-order equation that we propose or modify the Huang et al. model to reduce the number of parameters, embedding in the time-varying intraspecies coefficients all the adverse effects caused by microplastic particles. |
| first_indexed | 2024-03-09T09:52:59Z |
| format | Article |
| id | doaj.art-8a9d00f279f3484f8d13ca02742499bc |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T09:52:59Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-8a9d00f279f3484f8d13ca02742499bc2023-12-01T23:58:17ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472022-08-012746610.3390/mca27040066Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies CoefficientsLindomar Soares Dos Santos0José Renato Alcarás1Lucas Murilo Da Costa2Mateus Mendonça Ramos Simões3Alexandre Souto Martinez4Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida dos Bandeirantes, 3900, Ribeirão Preto 14040-901, SP, BrazilFaculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida dos Bandeirantes, 3900, Ribeirão Preto 14040-901, SP, BrazilFaculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida dos Bandeirantes, 3900, Ribeirão Preto 14040-901, SP, BrazilFaculdade de Medicina de Ribeirão Preto, Universidade de São Paulo, Avenida dos Bandeirantes, 3900, Ribeirão Preto 14049-900, SP, BrazilFaculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida dos Bandeirantes, 3900, Ribeirão Preto 14040-901, SP, BrazilDiscarded plastic is subjected to weather effects from different ecosystems and becomes microplastic particles. Due to their small size, they have spread across the planet. Their presence in living organisms can have several harmful consequences, such as altering the interaction between prey and predator. Huang et al. successfully modeled this system presenting numerical results of ecological relevance. Here, we have rewritten their equations and solved a set of them analytically, confirming that microplastic particles accumulate faster in predators than in prey and calculating the time values from which it happens. Using these analytical solutions, we have retrieved the Lotka–Volterra predator–prey model with time-varying intraspecific coefficients, allowing us to interpret ecological quantities referring to microplastics dispersion. After validating our equations, we solved analytically particular situations of ecological interest, characterized by extreme effects on predatory performance, and proposed a second-order differential equation as a possible next step to address this model. Our results open space for further refinement in the study of predator–prey models under the effects of microplastic particles, either exploring the second-order equation that we propose or modify the Huang et al. model to reduce the number of parameters, embedding in the time-varying intraspecies coefficients all the adverse effects caused by microplastic particles.https://www.mdpi.com/2297-8747/27/4/66microplasticsLotka–Volterrapredatorpreypredator–preypollution |
| spellingShingle | Lindomar Soares Dos Santos José Renato Alcarás Lucas Murilo Da Costa Mateus Mendonça Ramos Simões Alexandre Souto Martinez Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients Mathematical and Computational Applications microplastics Lotka–Volterra predator prey predator–prey pollution |
| title | Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients |
| title_full | Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients |
| title_fullStr | Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients |
| title_full_unstemmed | Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients |
| title_short | Analytical Solutions of Microplastic Particles Dispersion Using a Lotka–Volterra Predator–Prey Model with Time-Varying Intraspecies Coefficients |
| title_sort | analytical solutions of microplastic particles dispersion using a lotka volterra predator prey model with time varying intraspecies coefficients |
| topic | microplastics Lotka–Volterra predator prey predator–prey pollution |
| url | https://www.mdpi.com/2297-8747/27/4/66 |
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