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Wennergren, Uno
Publications (10 of 39) Show all publications
Andersson, J., Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2019). Density-Dependent Feedback in Age-Structured Populations. Journal of Mathematical Sciences, 242(1), 2-24
Open this publication in new window or tab >>Density-Dependent Feedback in Age-Structured Populations
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2019 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 242, no 1, p. 2-24Article in journal (Refereed) Published
Abstract [en]

The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2019
Keywords
Age-Structured Populations
National Category
Mathematics Other Biological Topics
Identifiers
urn:nbn:se:liu:diva-157057 (URN)
Available from: 2019-05-24 Created: 2019-05-24 Last updated: 2019-06-13Bibliographically approved
Ghersheen, S., Kozlov, V., Tkachev, V. & Wennergren, U. (2019). Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity. Mathematical methods in the applied sciences, 42(17), 5805-5826
Open this publication in new window or tab >>Dynamical behaviour of SIR model with coinfection: The case of finite carrying capacity
2019 (English)In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 42, no 17, p. 5805-5826Article in journal (Refereed) Published
Abstract [en]

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

Place, publisher, year, edition, pages
John Wiley & Sons, 2019
Keywords
carrying capacity, coinfection, global stability, linear complementarity problem, SIR model
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-160293 (URN)10.1002/mma.5671 (DOI)000496512900014 ()2-s2.0-85066086382 (Scopus ID)
Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2020-01-02Bibliographically approved
Kozlov, V., Tkachev, V., Vakulenko, S. & Wennergren, U. (2019). Global stability and persistence of complex foodwebs. Annali di Matematica Pura ed Applicata, 198(5), 1693-1709
Open this publication in new window or tab >>Global stability and persistence of complex foodwebs
2019 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 198, no 5, p. 1693-1709Article in journal (Refereed) Published
Abstract [en]

We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalizes some previous works and takes into account self-limitation. Under certain explicit conditions, we establish the global convergence and persistence of solutions.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Global stability, Persistence, Period-two-points, Non-increasing maps, Complex foodwebs, Self-limitation, Multiple resources
National Category
Mathematical Analysis Other Biological Topics
Identifiers
urn:nbn:se:liu:diva-155083 (URN)10.1007/s10231-019-00840-1 (DOI)000492034000012 ()
Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-11-11Bibliographically approved
Ghersheen, S., Kozlov, V., Tkachev, V. & Wennergren, U. (2019). Mathematical analysis of complex SIR model with coinfection and density dependence. Paper presented at 2019/09/17. Computational and Mathematical Methods, 1(4)
Open this publication in new window or tab >>Mathematical analysis of complex SIR model with coinfection and density dependence
2019 (English)In: Computational and Mathematical Methods, ISSN 2577-7408, Vol. 1, no 4Article in journal (Refereed) Published
Abstract [en]

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed, and several threshold conditions are obtained, which describes the establishment of diseases in the population. We prove that, for small carrying capacity K, there exists a globally stable disease-free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, that is, we prove that, (1) for small values of K, there exists a unique globally stable equilibrium point, and (b) it moves continuously as K is growing (while its face type may change). This indicates that the carrying capacity is the crucial parameter and an increase in resources in terms of carrying capacity promotes the risk of infection.

Place, publisher, year, edition, pages
Wiley-Blackwell Publishing Inc., 2019
Keywords
carrying capacity, coinfection, global stability, SIR model
National Category
Mathematics Immunology
Identifiers
urn:nbn:se:liu:diva-160284 (URN)10.1002/cmm4.1042 (DOI)
Conference
2019/09/17
Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2019-10-16Bibliographically approved
Kozlov, V., Vakulenko, S., Wennergren, U. & Tkachev, V. (2018). Biodiversity and robustness of large ecosystems. Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology, 36, 101-109
Open this publication in new window or tab >>Biodiversity and robustness of large ecosystems
2018 (English)In: Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology, ISSN 1476-945X, E-ISSN 1476-9840, Vol. 36, p. 101-109Article in journal (Refereed) Published
Abstract [en]

We study the biodiversity problem for resource competition systems with extinctions and self-limitationeffects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters ofthe model. We also prove the global stability of solutions for systems with extinctions and large turnoverrate. We show that when the extinction threshold is distinct from zero, the large time dynamics of systemis fundamentally non-predictable. In the last part of the paper we obtain explicit analytical estimates ofecosystem robustness with respect to variations of resource supply which support the R* rule for a systemwith random parameters.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Foodweb; Biodiversity; Global stability; Extinction threshold; Ecological networks; R* rule
National Category
Other Mathematics
Identifiers
urn:nbn:se:liu:diva-150011 (URN)10.1016/j.ecocom.2018.07.003 (DOI)000455065400011 ()
Note

Funding agencies: Linkoping University; Government of Russian Federation [08-08]; RFBR [16-01-00648]

Available from: 2018-08-07 Created: 2018-08-07 Last updated: 2019-01-21Bibliographically approved
Akram, U., Metson, G., Quttineh, N.-H. & Wennergren, U. (2018). Closing Pakistan’s yield gaps through nutrient recycling. Frontiers in Sustainable Food Systems, 1-14, Article ID 00024.
Open this publication in new window or tab >>Closing Pakistan’s yield gaps through nutrient recycling
2018 (English)In: Frontiers in Sustainable Food Systems, E-ISSN 2571-581X, p. 1-14, article id 00024Article in journal (Refereed) Published
Abstract [en]

Achieving food security will require closing yield gaps in many regions, including Pakistan. Although fertilizer subsidies have facilitated increased nitrogen (N) application rates, many staple crop yields have yet to reach their maximum potential. Considering that current animal manure and human excreta (bio-supply) recycling rates are low, there is substantial potential to increase the reuse of nutrients in bio-supply. We quantified 2010 crop N, phosphorus (P), and potassium (K) needs along with bio-supply nutrient availability for Pakistani districts, and compared these values to synthetic fertilizer use and costs. We found that synthetic fertilizer use combined with low bio-supply recycling resulted in a substantial gap between nutrient supply and P and K crop needs, which would cost 3 billion USD to fill with synthetic fertilizers. If all bio-supply was recycled, it could eliminate K synthetic fertilizer needs and decrease N synthetic fertilizer needs to 43% of what was purchased in 2010. Under a full recycling scenario, farmers would still require an additional 0.28 million tons of synthetic P fertilizers, costing 2.77 billion USD. However, it may not be prohibitively expensive to correct P deficiencies. Pakistan already spends this amount of money on fertilizers. If funds used for synthetic N were reallocated to synthetic P purchases in a full bio-supply recycling scenario, crop needs could be met. Most recycling could happen within districts, with only 6% of bio-supply requiring between-district transport when optimized to meet national N crop needs. Increased recycling in Pakistan could be a viable way to decrease yield gaps.

Place, publisher, year, edition, pages
Frontiers Media S.A., 2018
National Category
Environmental Sciences
Identifiers
urn:nbn:se:liu:diva-148786 (URN)10.3389/fsufs.2018.00024 (DOI)
Available from: 2018-06-19 Created: 2018-06-19 Last updated: 2018-09-14Bibliographically approved
Kozlov, V., Vakulenko, S. & Wennergren, U. (2016). Hamiltonian dynamics for complex food webs. PHYSICAL REVIEW E, 93(3), 032413
Open this publication in new window or tab >>Hamiltonian dynamics for complex food webs
2016 (English)In: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 93, no 3, p. 032413-Article in journal (Refereed) Published
Abstract [en]

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2016
National Category
Mathematics Biological Sciences
Identifiers
urn:nbn:se:liu:diva-127435 (URN)10.1103/PhysRevE.93.032413 (DOI)000372724300008 ()27078396 (PubMedID)
Note

Funding Agencies|Linkoping University, Government of Russian Federation [074-U01]; Russian Fund of Basic Research [16-01-00648]; US National Institutes of Health [RO1 OD010936]

Available from: 2016-05-01 Created: 2016-04-26 Last updated: 2016-05-17
Hakansson, N., Flisberg, P., Algers, B., Jonsson, A., Ronnqvist, M. & Wennergren, U. (2016). Improvement of animal welfare by strategic analysis and logistic optimisation of animal slaughter transportation. Animal Welfare, 25(2), 255-263
Open this publication in new window or tab >>Improvement of animal welfare by strategic analysis and logistic optimisation of animal slaughter transportation
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2016 (English)In: Animal Welfare, ISSN 0962-7286, Vol. 25, no 2, p. 255-263Article in journal (Refereed) Published
Abstract [en]

The transportation of animals to slaughterhouses is a major welfare concern. The number of slaughterhouses has decreased over time in Europe due to centralisation. This is expected to increase transport time for animals and as a consequence negatively affect animal welfare. We propose an optimisation model based on a facility location model to perform strategic analysis to improve transportation logistics. The model is tested on the Swedish slaughter transport system. We show that, by strategic planning and redirection of transports while keeping the slaughterhouse capacities as of the originaldata, the potential exists to reduce transport distance by 25% for pigs and 40% for cattle. Furthermore, we demonstrated that approximately 50% of Swedish slaughterhouses can be shut down with a minimal effect on total transport distances. This implies that in terms of the overall welfare picture, the decision of which animals to send where plays a for more significant role than the number of slaughterhouses. In addition, by changing relative weights on distances in the optimisation function the amount of individualtransports with longjourney times can be decreased. We also show results from altered slaughterhouse capacity and geographical location of slaughterhouses. This is the first time an entire country has been analysed in great detail with respect to the location, capacity and number of slaughterhouses. The focus is mainly on the analysis of unique and detailed information of actual animal transports in Sweden and a demonstration of the potential impact redirection of the transports and/ or altering of slaughterhouses can have on animal welfare.

Place, publisher, year, edition, pages
UNIV FEDERATION ANIMAL WELFARE, 2016
Keywords
animal welfare; cattle; pig; slaughterhouse capacity; slaughter transports; transportation logistics
National Category
Biological Sciences
Identifiers
urn:nbn:se:liu:diva-128729 (URN)10.7120/09627286.25.2.255 (DOI)000374841900011 ()
Note

Funding Agencies|Swedish board of Agriculture

Available from: 2016-06-01 Created: 2016-05-30 Last updated: 2017-11-30
Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2016). Persistence analysis of the age-structured population model on several patches. In: J. Vigo-Aguiar (Ed.), Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III: . Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016 (pp. 717-727). Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016. Universidad de Cádiz, 3
Open this publication in new window or tab >>Persistence analysis of the age-structured population model on several patches
2016 (English)In: Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III / [ed] J. Vigo-Aguiar, Universidad de Cádiz , 2016, Vol. 3, p. 717-727Chapter in book (Refereed)
Abstract [en]

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case and for periodically changing environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.

Place, publisher, year, edition, pages
Universidad de Cádiz, 2016
Keywords
age-structure, persistence, Kermack-McKendrick equation, Lotcka-Volterra equation
National Category
Biological Sciences Mathematics
Identifiers
urn:nbn:se:liu:diva-130231 (URN)9788460860822 (ISBN)
Conference
Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016
Note

Associate Editors

P. Schwerdtfeger (New Zealand), W. Sprößig (Germany), N. Stollenwerk (Portugal), Pino Caballero (Spain), J. Cioslowski (Poland), J. Medina (Spain), I. P. Hamilton (Canada), J. A. Alvarez-Bermejo (Spain)

Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2016-08-31Bibliographically approved
Gudmundson, S., Eklöf, A. & Wennergren, U. (2015). Environmental variability uncovers disruptive effects of species interactions on population dynamics. Proceedings of the Royal Society of London. Biological Sciences, 282(1812), 67-75
Open this publication in new window or tab >>Environmental variability uncovers disruptive effects of species interactions on population dynamics
2015 (English)In: Proceedings of the Royal Society of London. Biological Sciences, ISSN 0962-8452, E-ISSN 1471-2954, Vol. 282, no 1812, p. 67-75Article in journal (Refereed) Published
Abstract [en]

How species respond to changes in environmental variability has been shown for single species, but the question remains whether these results are transferable to species when incorporated in ecological communities. Here, we address this issue by analysing the same species exposed to a range of environmental variabilities when (i) isolated or (ii) embedded in a food web. We find that all species in food webs exposed to temporally uncorrelated environments (white noise) show the same type of dynamics as isolated species, whereas species in food webs exposed to positively autocorrelated environments (red noise) can respond completely differently compared with isolated species. This is owing to species following their equilibrium densities in a positively autocorrelated environment that in turn enables species species interactions to come into play. Our results give new insights into species response to environmental variation. They especially highlight the importance of considering both species interactions and environmental autocorrelation when studying population dynamics in a fluctuating environment.

Place, publisher, year, edition, pages
ROYAL SOC, 2015
Keywords
environmental autocorrelation; environmental tracking; food webs; indirect effects; paradox of enrichment; population stability
National Category
Biological Sciences
Identifiers
urn:nbn:se:liu:diva-122442 (URN)10.1098/rspb.2015.1126 (DOI)000362305500008 ()26224705 (PubMedID)
Note

Funding Agencies|Linkoping University

Available from: 2015-11-03 Created: 2015-11-02 Last updated: 2017-12-01
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