An immuno-eco-epidemiological model of competition. (English) Zbl 1448.92277
Summary: This paper introduces a novel immuno-eco-epidemiological model of competition in which one of the species is affected by a pathogen. The infected individuals from species one are structured by time-since-infection and the within-host dynamics of the pathogen and the immune response is also modelled. A novel feature of the model is the impact of the species two numbers on the ability of species one to mount an immune response. The within-host model has three equilibria: an extinction equilibrium, pathogen-only equilibrium and pathogen and immune response equilibrium which exists if the immune response reproduction number \(R_0>1\). The extinction equilibrium is always unstable, the pathogen-only equilibrium is stable if \(R_0<1\), and the coexistence equilibrium is stable whenever it exists. The between-host competition model has six equilibria: an extinction equilibrium, three disease-free equilibria: species one-only equilibrium, species two-only equilibrium and a disease-free species coexistence equilibrium. There are also two disease-present equilibria: species one-only disease equilibrium and disease coexistence equilibrium. The existence and stability of these equilibria are governed by six reproduction numbers. Results show that for a non-fatal disease, the disease coexistence equilibrium is stable whenever it exists.
Keywords:
immunology; epidemiology; ecology; competition; multiscale modeling; immuno-eco-epidemiologyReferences:
| [1] | S. Alizon and S. Lion, Within-host parasite cooperation and the evolution of virulence, Proc. R. Soc. London, Ser. B 278 (2011), pp. 3738-3747. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [2] | S. Alizon, F. Luciani, and R.R. Regoes, Epidemiological and clinical consequences of within-host evolution, Trends Microbiol. 19 (2011), pp. 24-32. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [3] | American Psychological Association, Stress weakens the immune system, Available at http://www.apa.org/research/action/immune.aspx. [Google Scholar] |
| [4] | R.M. Anderson and R.M. May, The invasion, persistence and spread of infectious diseases within animal and plant communities, Philos Trans R Soc Lond B Biol Sci. 314(1167) (1986), pp. 533-570. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [5] | J.-B. André and S. Gandon, Vaccination, within-host dynamics, and virulence evolution, Evolution 60(1) (2006), pp. 13-23. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [6] | O. Angulo, F. Milner, and L. Sega, A SIR epidemic model structured by immunological variables, J. Biol. Syst. 21 (2013), p. 1340013. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1342.92223 |
| [7] | O. Angulo, F.A. Milner, and L.M. Sega, Immunological models of epidemics, MACI (Matematica Aplicada, Computacional e Industrial) 4 (2013), pp. 53-56. [Google Scholar] |
| [8] | R. Antia, B.R. Levin, and R.M. May, Within-host population dynamics and the evolution and maintenance of microparasite virulence, Amer. Nat. 144(3) (1994), pp. 457-472. [Crossref], [Web of Science ®], [Google Scholar] |
| [9] | W.E. Armstrong, White-tailed deer competition with goats, sheep, cattle and exotic wildlife, in Wildlife Management Handbook, 2011, pp. V-A1-V-A4. Available at http://roberts.agrilife.org/files/2011/06/whitetailed_deer_competitionother_animals_17.pdf. [Google Scholar] |
| [10] | M. Begon, R.G. Bowers, N. Kadianakis, and D.E. Hodgkinson, Disease and community structure: The importance of host self-regulation in a host-host-pathogen model, Amer. Nat. 139 (1992), pp. 1131-1150. [Crossref], [Web of Science ®], [Google Scholar] |
| [11] | S. Bhattacharya, M. Martcheva, and X.-Z. Li, A predator-prey-disease model with immune response in infected prey, J. Math. Anal. Appl. 411(1) (2014), pp. 297-313. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1308.92080 |
| [12] | M.B. Bonsall and R.D. Holt, Apparent competition and vector-host interactions, Israel J. Ecol. Evol. 56 (2010), pp. 393-416. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] |
| [13] | T.A. Campbell and K.C. VerCauteren, Diseases and parasites, in Biology and management of White-Tailed Deer, D. Hewitt, ed., Boca Raton, FL, CRC Press, 2011, pp. 219-249. [Google Scholar] |
| [14] | X. Cen, Z. Feng, and Y. Zhao, Emerging disease dynamics in a model coupling within-host and between-host systems, JTB 361 (2014), pp. 141-151. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1303.92113 |
| [15] | Centers for Disease Control and Prevention, National center for emerging and zoonotic infectious diseases, Available at http://www.cdc.gov/ncezid/. [Google Scholar] |
| [16] | J. Chattopadhyay and O. Arino, A predator-prey model with disease in the prey, Nonlinear Anal. 36 (1999), pp. 747-766. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 0922.34036 |
| [17] | D. Coombs, M.A. Gilchrist, and C.L. Ball, Evaluating the importance of within- and between-host selection pressures on the evolution of chronic pathogens, Theoret. Popul. Biol. 72 (2007), pp. 576-591. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1141.92036 |
| [18] | T. Day, S. Alizon, and N. Mideo, Bridging scales in the evolution of infectious disease life histories: theory, Evolution 65 (2011), pp. 3448-3461. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [19] | S. DebRoy and M. Martcheva, Immuno-epidemiology and HIV/AIDS: A Modeling prospective, in Mathematical Biology Research Trends, L.B. Wilson, ed., Nova Publishers, New York, 2008, pp. 175-192. [Google Scholar] |
| [20] | P. van den Driessche and M.L. Zeeman, Disease induced oscillations between two competing species, SIAM J. Appl. Dyn. Syst. 3 (2004), pp. 601-619. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1055.92058 |
| [21] | J. Dushoff, Incorporating immunological ideas in epidemiological models, J. Theoret. Biol. 180 (1996), pp. 181-187. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [22] | Z. Feng, J. Velasco-Hernandez, B. Tapia-Santos, and M. Leite, A model for coupling within-host and between-host dynamics in an infectious disease, Nonlinear Dyn. 68 (2011), pp. 401-411. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1254.92077 |
| [23] | Z. Feng, J. Velasco-Hernandez, and B. Tapia-Santos, A mathematical model for coupling within-host and between-host dynamics in an environmentally-driven infectious disease, MBS 241(1) (2013), pp. 49-55. [Google Scholar] · Zbl 1309.92066 |
| [24] | A. Gandolfi, A. Pugliese, and C. Sinisgalli, Epidemic dynamics and host immune response: a nested approach, J. Math. Biol. 70(3) (2015), pp. 399-435. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1307.92341 |
| [25] | V.V. Ganusov, C.T. Bergstrom, and R. Antia, Within-host population dynamics and the evolution of microparasites in a heterogeneous host population, Evolution 56 (2002), pp. 213-223. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [26] | M.A. Gilchrist and D. Coombs, Evolution of virulence: Interdependence, constraints, and selection using nested models, Theoret. Pop. Biol. 69 (2006), pp. 145-153. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1089.92044 |
| [27] | M.A. Gilchrist and A. Sasaki, Modeling host-parasite coevolution: a nested approach based on mechanistic models, J. Theoret. Biol. 218 (2002), pp. 289-308. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [28] | K.P. Hadeler and H.I. Freedman, Predator-prey populations with parasitic infection, J. Math. Biol. 27 (1989), pp. 609-631. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 0716.92021 |
| [29] | M.J. Hatcher and A.M. Dunn, Parasites in Ecological Communities: From Interactions to Ecosystems, Cambridge University Press, Cambrige, 2011. [Crossref], [Google Scholar] |
| [30] | B. Hellriegel, Immunoepidemiology: Bridging the gap between immunology and epidemiology, Trends Parasitol. 17 (2001), pp. 102-106. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [31] | R.D. Holt and M. Barfield, Within-host pathogen dynamics: Some ecological and evolutionary consequences of transients, dispersal mode, and within-host spatial heterogeneity, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 71 (2006), pp. 45-66. [Google Scholar] · Zbl 1152.92346 |
| [32] | R.D. Holt and J. Pickering, Infectious disease and species coexistence: a model of Lotka-Volterra form, Amer. Nat. 126 (1985), pp. 196-211. [Crossref], [Web of Science ®], [Google Scholar] |
| [33] | R.D. Holt and M. Roy, Predation can increase the prevalence of infectious disease, Amer. Nat. 169 (2007), pp. 690-699. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [34] | G.L. Johnston, D.L. Smith, D.A. Fidock, and R. Antia, Malaria’s missing number: calculating the human component of ##img####img####img##R0 by a within-host mechanistic model of Plasmodium falciparum infection and transmission, PLOS Comput. Biol. 9(4) (2013), p. e1003025. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [35] | M.J. Keeling and P. Rohani, Modelling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, NJ, 2008. [Crossref], [Google Scholar] · Zbl 1279.92038 |
| [36] | T. Kostova, Persistence of viral infections on the population level explained by an immunoepidemiological model, Math. Biosci. 206 (2007), pp. 309-319. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1114.92046 |
| [37] | P. Lemey, A. Rambaut, and O. Pybus, HIV evolutionary dynamics within and among hosts, AIDS Rev. 8 (2006), pp. 125-140. [PubMed], [Web of Science ®], [Google Scholar] |
| [38] | F. Luciani, S. Alizon, and C. Fraser, The evolutionary dynamics of a rapidly mutating virus within and between hosts: The case of hepatitis C virus, PLoS Comput. Biol. 5 (2009), p. e1000565. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [39] | M. Martcheva, Evolutionary consequences of predation for pathogens in prey, Bull. Math. Biol. 71(4) (2009), pp. 819-844. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1163.92039 |
| [40] | M. Martcheva, An Immuno-epidemiological model of paratuberculosis, AIP Conf. Proc. 1404 (2011), pp. 176-183. [Crossref], [Google Scholar] |
| [41] | M. Martcheva, An evolutionary model of influenza a with drift and shift, J. Biol. Dyn. 6(2) (2012), pp. 299-332. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1447.92289 |
| [42] | M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York, 2015. [Crossref], [Google Scholar] · Zbl 1333.92006 |
| [43] | M. Martcheva and X.-Z. Li, Linking immunological and epidemiological dynamics of HIV: the case of super-infection, J. Biol. Dyn. 7(1) (2013), pp. 161-182. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1447.92451 |
| [44] | M. Martcheva and S.S. Pilyugin, An epidemic model structured by host immunity, J. Biol. Syst. 14 (2006), pp. 185-203. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1105.92032 |
| [45] | M. Martcheva, S. Lenhart, S. Eda, D. Klinkenberg, E. Momotani, and J. Stable, An Immuno-epidemiological models for Johne’s disease in cattle, Vet. Res. 46 (2015), p. 69. [Google Scholar] |
| [46] | N. Mideo, S. Alizon, and T. Day, Linking within- and between-host dynamics in the evolutionary epidemiology of infectious diseases, Trends Ecol. Evol. 23 (2008), pp. 511-517. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
| [47] | F.A. Milner and L.M. Sega, Integrating immunological and epidemiological models, in 18th World IMACS/MODSIM Congress, Cairns, Australia, 13-17 July 2009. Available at http://mssanz.org.au/modsim09. [Google Scholar] |
| [48] | E. Numfor, S. Bhattacharya, S. Lenhart, and M. Martcheva, Optimal control of nested within-host and between-host model, Math. Model. Nat. Phenom. 7(2) (2014), pp. 171-203. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1294.49013 |
| [49] | R.S. Ostfeld, F. Keesing, and V.T. Eviner, The ecology of infectious diseases: progress, challenges, and frontiers, in Infectious Disease Ecology: Effects of Ecosystems on Disease and of Disease on Ecosystems, R.S. Ostfeld, F. Keesing, and V. Eviner, eds., Princeton University press, Princeton, NJ, 2008, pp. 469-482. [Google Scholar] |
| [50] | A. Pugliese, The role of host population heterogeneity in the evolution of virulence, J. Biol. Dyn. 5 (2011), pp. 104-119. [Taylor & Francis Online], [Google Scholar] · Zbl 1403.92308 |
| [51] | M. Roy and R.D. Holt, Effects of predation on host-pathogen dynamics in SIR models, Theoret. Popul. Biol. 73 (2008), pp. 319-331. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1209.92054 |
| [52] | D. Stiefs, E. Venturino, and U. Feudel, Evidence of chaos in eco-epidemic models, Math. Biosci. Eng. 6 (2009), pp. 855-871. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1178.92057 |
| [53] | D.M. Vickers and N.D. Osgood, A unified framework of immunological and epidemiological dynamics for the spread of viral infections in a simple network-based population, Theoret. Biol. Med. Model. 4 (2007), p. 49. [Crossref], [PubMed], [Web of Science ®], [Google Scholar] |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
