The usefulness of mathematics in agriculture, for the environment and in contrasting diseases: insights from a wide range of simple models

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2 S. Zytynska and E. Venturino, Modelling multispecies interactions and horizontal transmission of aphid bacterial symbionts, Riv Matem Univ Parma, vol. 12, no. 2, pp. 327–383, 2021. Search in Google Scholar

3 E. Venturino, M. Isaia, F. Bona, S. Chatterjee, and G. Badino, Biological controls of intensive agroecosystems: Wanderer spiders in the langa astigiana, Ecological Complexity, vol. 5, pp. 157–164, 2008. Search in Google Scholar

4 E. Venturino, M. Isaia, E. Issoglio, V. Triolo, and G. Badino, Modelling the spiders ballooning effect on the vineyard ecology, Math Modelling Natural Phenomena, vol. 1, no. 1, pp. 137–159, 2006. Search in Google Scholar

5 S. Pappalardo, M. Villa, S. Santos, J. Benhadi-Marín, J. Pereira, and E. Venturino, A tritrophic interaction model for an olive tree pest, the olive moth Prays oleae (Bernard), Ecological Modelling, vol. 462, p. 10977, 2021. Search in Google Scholar

6 A. Rosso and E. Venturino, A dynamic programming approach to ecosystem management, Algorithms, vol. 16, no. 3, p. 139, 2023. Search in Google Scholar

7 M. F. J. Cerri and S. Bertolino, Rabbits killing hares: An invasive mammal modifies native predator-prey dynamics, Animal Conservation, vol. 20, pp. 511–519, 2017. Search in Google Scholar

8 E. Caudera, S. Viale, S. Bertolino, J. Cerri, and E. Venturino, A mathematical model supporting a hyperpredation effect in the apparent competition between invasive eastern cottontail and native european hare, Bull. Math.Biol., vol. 83, no. 51, 2021. Search in Google Scholar

9 V. L. Morgia and E. Venturino, Understanding hybridization and competition processes between hare species: implications for conservation and management on the basis of a mathematical model, Ecological Modeling, vol. 364, pp. 13–24, 2017. Search in Google Scholar

10 V. Ajraldi, M. Pittavino, and E. Venturino, Modelling herd behavior in population systems, Nonlinear Analysis Real World Applications, vol. 12, pp. 2319–2338, 2011. Search in Google Scholar

11 M. L. Rosenzweig and R. H. MacArthur, Graphical representation and stability conditions of predator-prey interactions, The American Naturalist, vol. 97, pp. 209–223, 1963. Search in Google Scholar

12 E. Venturino and S. Petrovskii, Spatiotemporal behavior of a prey-predator system with a group defense for prey, Ecological Complexity, vol. 14, pp. 37–47, 2013. Search in Google Scholar

13 C. Cosner, D. L. DeAngelis, J. S. Ault, and D. B. Olson, Effects of spatial grouping on the functional response of predators, Theor Popul Biol, vol. 56, no. 1, pp. 65–75, 1999. Search in Google Scholar

14 D. Melchionda, E. Pastacaldi, C. Perri, M. Banerjee, and E. Venturino, Social behavior-induced multistability in minimal competitive ecosystems, J. Theoretical Biology, vol. 439, pp. 24–38, 2018. Search in Google Scholar

15 F. Acotto and E. Venturino, Modeling the herd prey response to individualistic predators attacks, Math. Meth. Appl. Sci., vol. 46, no. 12, pp. 13436–13456., 2023. Search in Google Scholar

16 F. Acotto and E. Venturino, How do predator interference, prey herding and their possible retaliation affect prey-predator coexistence?, AIMS Mathematics, vol. 9, no. 7, pp. 17122–17145, 2024. Search in Google Scholar

17 F. Acotto, L. Bardi, A. Manzini, O. Sarfatti, A. Viscardi, and E. Venturino, An exploration of the effects of periodic top predator interference and hunting on a predator-prey system, in Trends in Biomathematics - Selected Works from the BIOMAT Consortium Lectures (R. P. Mondaini, ed.), Springer, Cham, Switzerland, 2024. Search in Google Scholar

18 F. Acotto, A. Viscardi, and E. Venturino, Does a marginal contact with a native species living in a complex domain with a fractional dimension boundary represent a sufficient invasive mechanism for the establishment of a migrating population?, Chaos, Solitons & Fractals, vol. 184, p. 115050, 2024. Search in Google Scholar

19 R. Cavoretto, A. De Rossi, E. Perracchione, and E. Venturino, Robust approximation algorithms for the detection of attraction basins in dynamical systems, J Sci Comput, vol. 68, pp. 395–415, 2016. Search in Google Scholar

20 R. Cavoretto, A. De Rossi, E. Perracchione, and E. Venturino, Graphical representation of separatrices of attraction basins in two and three dimensional dynamical systems, Int. J. Computational Methods, vol. 14, p. 1750008, 2017. Search in Google Scholar

21 G. Sabetta, E. Perracchione, and E. Venturino, Wild herbivores in forests: four case studies, in Biomat 2014 (R. Mondaini, ed.), pp. 55–57, World Scientific, 2015. Search in Google Scholar

22 Y. Sekerci and S. Petrovskii, Mathematical modelling of plankton-oxygen dynamics under the climate change, Bulletin of Mathematical Biology, vol. 77, no. 12, pp. 2325–2353, 2015. Search in Google Scholar

23 Y. Sekerci, S. Petrovskii, and E. Venturino, Regime shifts and ecological catastrophes in a model of plankton-oxygen dynamics under the climate change, J. of Theoretical Biology, vol. 424, pp. 91–109, 2017. Search in Google Scholar

24 S. A. Vakulenko, I. Sudakov, S. V. Petrovskii, and D. Lukichev, Stability of a planetary climate system with the biosphere species competing for resources, Phys. Rev. E, vol. 103, p. 022, 2021. Search in Google Scholar

25 I. Sudakow, S. A. Vakulenko, M. Pound, and D. Kirievskaya, Biome stability and fragmentation under critical environmental temperature change, Appl. Math. Model, vol. 114, pp. 189–204, 2023. Search in Google Scholar

26 P. D. Ditlevsen and S. Ditlevsen, Warning of a forthcoming collapse of the Atlantic Meridional Overturning Circulation, Nature Communications, vol. 14, no. 1, p. 4254, 2023. Search in Google Scholar

27 A. E. Nelson, K. Ravichandran, and U. Antony, The impact of the Green Revolution on indigenous crops of India, J. Ethn. Food, vol. 6, no. 8, 2019. Search in Google Scholar

28 I. M. Bulai, F. Spina, G. C. Varese, and E. Venturino, Wastewater bioremediation using white rot fungi: validation of a dynamical system with real data obtained in laboratory, Math Meth Appl Sci., vol. 41, pp. 4195–4207, 2018. Search in Google Scholar

29 C. Berardo, I. M. Bulai, P. Baptista, T. Gomes, and E. Venturino, Modeling the endophytic fungus Epicoccum nigrum action to fight the “olive knot” disease caused by Pseudomonas savastanoi pv. savastanoi (Psv) bacteria in Olea europaea trees, in Trends in Biomathematics: Modeling, Optimization and Computational Problems Selected Works from the Biomat Consortium Lectures, Moscow 2017 (R. Mondaini, ed.), pp. 189–207, Springer, 2018. Search in Google Scholar

30 P. Baptista,, I. M. Bulai, T. Gomes, and E. Venturino, Modeling the interactions among phythopatogens and phyllosphere microorganisms for the biological disease control of Olea europaea l., Mathematical Biosciences, vol. 308, no. 6, pp. 42–58, 2019. Search in Google Scholar

31 M. Pittavino, L. Ferreri, E. Venturino, M. Giacobini, L. Bertolotti, and S. Rosati, Influence of small ruminant lentivirus infection on the replacement rate in goat breeding, Hystrix It. J. Mamm., vol. supp, p. 169, 2012. Search in Google Scholar

32 M. Pittavino, L. Ferreri, M. Giacobini, L. Bertolotti, S. Rosati, and E. Venturino, A CAEV epidemiological model for goat breeding, Applied Mathematics and Computation, vol. 227, pp. 156–163, 2014. Search in Google Scholar

33 S. Collino, E. Venturino, L. Ferreri, L. Bertolotti, S. Rosati, and M. Giacobini, Models for two strains of the Caprine Arthritis Encephalitis Virus Disease, in Biomat 2015 (R. Mondaini, ed.), pp. 297–318, World Scientific, 2016. Search in Google Scholar

34 S. Collino, E. Venturino, L. Ferreri, L. Bertolotti, S. Rosati, and M. Giacobini, An effective management strategy for the control of two lentiviruses in goat breedings, J. Theoretical Biology, vol. 469, pp. 96–106, 2019. Search in Google Scholar

35 B. W. Kooi and E. Venturino, Ecoepidemic predator-prey model with feeding satiation, prey herd behavior and abandoned infected prey, Math. Biosc, vol. 274, pp. 58–72, 2016. Search in Google Scholar

36 E. Cagliero and E. Venturino, Ecoepidemics with infected prey in herd defense: the harmless and toxic cases, International Journal of Computer Mathematics, vol. 93, no. 1, pp. 108–127, 2016. Search in Google Scholar

37 A. White, S. S. Bell, P. W. W. Lurz, and M. Boots, Conservation management within strongholds in the face of disease-mediated invasions: red and grey squirrels as a case study, Journal of Applied Ecology, vol. 51, no. 6, pp. 1631–1642, 2014. Search in Google Scholar

38 D. M. Tompkins, A. R. White, and M. Boots, Ecological replacement of native red squirrels by invasive greys driven by disease, Ecology Letters, vol. 6, no. 3, pp. 189–196, 2003. Search in Google Scholar

39 A. Gosso, V. La Morgia, P. Marchisio, O. Telve, and E. Venturino, Does a larger carrying capacity for an exotic species allow environment invasion? — Some considerations on the competition of red and grey squirrels, J. of Biol. Systems, vol. 20, no. 3, pp. 221–234, 2012. Search in Google Scholar

40 F. Barbara, V. La Morgia, V. Parodi, G. Toscano, and E. Venturino, Analysis of the incidence of poxvirus on the dynamics between red and grey squirrels, Mathematics, 2018, 6,, vol. 6, p. 113, 2018. Search in Google Scholar

41 E. Travaglia, V. La Morgia, and E. Venturino, Poxvirus, red and grey squirrel dynamics: is the recovery of a common predator affecting system equilibria? Insights from a predator-prey ecoepidemic model, Discrete and Continuous Dynamical Systems, vol. 25, no. 6, pp. 2023–2040, 2020. Search in Google Scholar

42 V. Capasso and G. Serio, A Generalization of the Kermack-Mckendrick deterministic epidemic model, Math. Biosci., vol. 42, pp. 43–61, 1978. Search in Google Scholar

43 A. d’Onofrio and P. Manfredi, Behavioral SIR models with incidence-based social-distancing, Chaos Solitons & Fractals, vol. 159, p. 112072, 2022. Search in Google Scholar

44 A. d’Onofrio, P. Manfredi, and P. Poletti, The interplay of public intervention and private choices in determining the outcome of vaccination programmes, PLoS ONE, vol. 7, p. e45653, 2012. Search in Google Scholar

45 A. d’Onofrio and P. Manfredi, Modeling the Interplay between Human Behavior and the Spread of Infectious Diseases. Springer, 2013. Search in Google Scholar

46 F. Acotto and E. Venturino, A note on an epidemic model with cautionary response in the presence of asymptomatic individuals, Axioms, vol. 12, no. 1, p. 62, 2023. Search in Google Scholar