92D30, 92D40.

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

Competing species models with an infectious disease

1. Applied Mathematical and Computational Sciences, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242

Abstract    Related pages

The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number $\mathbf{R}_1$ determines the asymptotic behavior, so that the disease dies out if $\mathbf{R}_1 \leq 1$ and approaches a globally attractive endemic equilibrium if $\mathbf{R}_1 > 1$. Because the disease- reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.
Figure/Table
Supplementary
Article Metrics

Citation: Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences and Engineering, 2006, 3(1): 219-235. doi: 10.3934/mbe.2006.3.219

• 1. Udai Kumar, Partha Sarathi Mandal, E. Venturino, Impact of Allee effect on an eco-epidemiological system, Ecological Complexity, 2020, 42, 100828, 10.1016/j.ecocom.2020.100828
• 2. Litao Han, Andrea Pugliese, Epidemics in two competing species, Nonlinear Analysis: Real World Applications, 2009, 10, 2, 723, 10.1016/j.nonrwa.2007.11.005
• 3. Jeewoen Shin, Thomas MacCarthy, Potential for evolution of complex defense strategies in a multi-scale model of virus-host coevolution, BMC Evolutionary Biology, 2016, 16, 1, 10.1186/s12862-016-0804-z
• 4. Yicheng Liu, Yimin Du, Jianhong Wu, Backward/Hopf bifurcations in SIS models with delayed nonlinear incidence rates, Frontiers of Mathematics in China, 2008, 3, 4, 535, 10.1007/s11464-008-0040-y
• 5. Sally S. Bell, Andrew White, Jonathan A. Sherratt, Mike Boots, Invading with biological weapons: the role of shared disease in ecological invasion, Theoretical Ecology, 2009, 2, 1, 53, 10.1007/s12080-008-0029-x
• 6. Maia Martcheva, Evolutionary Consequences of Predation for Pathogens in Prey, Bulletin of Mathematical Biology, 2009, 71, 4, 819, 10.1007/s11538-008-9383-5
• 7. F. B. AGUSTO, K. O. OKOSUN, OPTIMAL SEASONAL BIOCONTROL FOREICHHORNIA CRASSIPES, International Journal of Biomathematics, 2010, 03, 03, 383, 10.1142/S1793524510001021
• 8. , Stochastic models for competing species with a shared pathogen, Mathematical Biosciences and Engineering, 2012, 9, 3, 461, 10.3934/mbe.2012.9.461
• 9. Nidhi Parikh, Mina Youssef, Samarth Swarup, Stephen Eubank, Modeling the effect of transient populations on epidemics in Washington DC, Scientific Reports, 2013, 3, 1, 10.1038/srep03152
• 10. V. A. BOKIL, C. A. MANORE, LINKING POPULATION DYNAMICS AND DISEASE MODELS FOR MULTI-HOST PATHOGEN SYSTEMS: IMPLICATIONS FOR PATHOGEN AND SPECIES INVASION, Journal of Biological Systems, 2013, 21, 04, 1340011, 10.1142/S0218339013400111
• 11. E. Venturino, V. Volpert, Ecoepidemiology: a More Comprehensive View of Population Interactions, Mathematical Modelling of Natural Phenomena, 2016, 11, 1, 49, 10.1051/mmnp/201611104