×

Effects of predation on host-pathogen dynamics in SIR models. (English) Zbl 1209.92054

Summary: The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a “hump”-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. We examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.

MSC:

92D30 Epidemiology
92D40 Ecology
34D20 Stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology

Software:

MATCONT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abrams, P. A., Will small population sizes warn us of impending extinctions?, Am. Nat., 160, 293-305 (2002)
[2] Anderson, R. M.; May, R. M., The invasion, persistence and spread of infectious diseases within animal and plant communities, Phil. Trans. R. Soc. Lond., B 314, 533-570 (1986)
[3] Arneberg, P.; Skorping, A.; Grenfell, B.; Read, A. F., Host densities as determinants of abundance in parasite communities, Proc. R. Soc. Lond. B, 265, 1283-1289 (1998)
[4] Borer, E. T.; Briggs, C. J.; Holt, R. D., Predators, parasitoids, and pathogens: A cross-cutting examination of intraguild predation theory, Ecology, 88, 2681-2688 (2007)
[5] Braza, P. A., Predator-prey dynamics with disease in the prey, Math. Biosci. Eng., 2, 703-717 (2005) · Zbl 1110.34030
[6] Chattopadhyay, J.; Arino, O., A predator-prey model with disease in the prey, Nonlinear Anal., 36, 747-766 (1999) · Zbl 0922.34036
[7] Chattopadhyay, J.; Pal, S.; Abdllaoui, A. E., Classical predator-prey system with infection of prey population — a mathematical model, Math. Methods Appl. Sci., 26, 1211-1222 (2003) · Zbl 1044.34001
[8] Childs, J. E.; Glass, G. E.; Korch, G. W.; LeDuc, J. W., Effects of hantaviral infection on survival, growth and fertility in wild rat (Rattus norvegicus) populations of Baltimore, Maryland, J. Wildlife Diseases, 25, 469-476 (1989)
[9] Collinge, S. K.; Ray, C., Disease Ecology: Community Structure and Pathogen Dynamics (2006), Oxford University Press: Oxford University Press NY
[10] DeAngelis, D. L.; Goldstein, R. L.; O’Neill, R. V., A model for trophic interaction, Ecology, 56, 881-892 (1975)
[11] de Castro, F.; Bolker, B. M., Parasite establishment and host extinction in model communities, Oikos, 111, 501-513 (2005)
[12] Dhooge, A.; Govaerts, W.; Kuznetsov, Y. A., MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM TOMS, 29, 141-164 (2003) · Zbl 1070.65574
[13] Dobson, A. P., Population dynamics of pathogens with multiple host species, Am. Nat. (Suppl.), 164, S64-S78 (2004)
[14] Dwyer, G.; Dushoff, J.; Yee, S. H., The combined effects of pathogens and predators on insect outbreaks, Nature, 430, 341-345 (2004)
[15] Edelstein-Keshet, L., Mathematical Models in Biology (1988), Random House: Random House New York · Zbl 0674.92001
[16] Hall, S. R.; Duffy, M. A.; Cáceres, C. E., Selective predation and productivity jointly drive complex behavior in host-parasite systems, Am. Nat., 165, 70-81 (2005)
[17] Han, L.; Ma, Z.; Hethcote, H. W., Four predator-prey models with infectious diseases, Math. Comput. Modelling, 34, 849-858 (2001) · Zbl 0999.92032
[18] Hethcote, H. W.; Wang, W.; Han, L.; Ma, Z., A predator-prey model with infected prey, Theor. Popul. Biol., 66, 259-268 (2004)
[19] Hochberg, M. E.; Hassell, M. P.; May, R. M., The dynamics of host-parasitoid-pathogen interactions, Am. Nat., 135, 74-94 (1990)
[20] Holt, R. D.; Dobson, A. P., Extending the principles of community ecology to address the epidemiology of host-pathogen systems, (Collinge, S. K.; Ray, C., Disease Ecology: Community Structure and Pathogen Dynamics (2006), Oxford University Press: Oxford University Press NY), 6-27
[21] Holt, R. D.; Polis, G. A., A theoretical framework for intraguild predation, Am. Nat., 149, 745-764 (1997)
[22] Holt, R. D.; Roy, M., Predation can increase the prevalence of infectious disease, Am. Nat., 169, 690-699 (2007)
[23] Hudson, P. J.; Dobson, A. P.; Newborn, D., Do parasites make prey vulnerable to predation? Red grouse and parasites, J. Animal Ecology, 61, 681-692 (1992)
[24] Keesing, F.; Holt, R. D.; Ostfeld, R. S., Effects of species diversity on disease risk, Ecol. Lett., 9, 485-498 (2006)
[25] Murdoch, W. W.; Briggs, C. J.; Nisbet, R. M., Consumer-Resource Dynamics (2003), Princeton University Press: Princeton University Press Princeton, NJ
[26] Ostfeld, R. S.; Holt, R. D., Are predators good for your health? Evaluating evidence for top-down regulation of zoonotic disease reservoirs, Frontiers Ecol. Environ., 2, 13-20 (2004)
[27] Packer, C.; Holt, R. D.; Dobson, A. P.; Hudson, P., Keeping the herds healthy and alert: Impacts of predation upon prey with specialist pathogens, Ecol. Lett., 6, 797-802 (2003)
[28] Rohani, P., Wearing, H.J., Vasco, D.A., Huang, Y., Understanding host-multi-pathogen systems: the interaction between ecology and immunology. In: Ostfeld, R.S., Keesing, F., Eviner, V. (Eds.), Ecology of Infectious Diseases, Princeton University Press, NJ (in press); Rohani, P., Wearing, H.J., Vasco, D.A., Huang, Y., Understanding host-multi-pathogen systems: the interaction between ecology and immunology. In: Ostfeld, R.S., Keesing, F., Eviner, V. (Eds.), Ecology of Infectious Diseases, Princeton University Press, NJ (in press)
[29] Rosenzweig, M. L., The paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science, 171, 385-387 (1971)
[30] Turchin, P., Complex Population Dynamics (2003), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 1062.92077
[31] Wolf, A.; Swift, J. B.; Swinney, H. L.; Vastano, J. A., Determining lyapunov exponents from a time series, Physica D, 16, 285-317 (1985) · Zbl 0585.58037
[32] Woolhouse, M. E.J.; Taylor, L. H.; Haydon, D. T., Population biology of multihost pathogens, Science, 292, 1109-1112 (2001)
[33] Xiao, Y.; Chen, L., Modeling and analysis of a predator-prey model with disease in the prey, Math. Biosci., 171, 59-82 (2001) · Zbl 0978.92031
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.