×

Global dynamics of a host-vector-predator mathematical model. (English) Zbl 1437.92150

Summary: A mathematical model which links predator-vector(prey) and host-vector theory is proposed to examine the indirect effect of predators on vector-host dynamics. The equilibria and the basic reproduction number \(R_0\) are obtained. By constructing Lyapunov functional and using LaSalle’s invariance principle, global stability of both the disease-free and disease equilibria are obtained. Analytical results show that \(R_0\) provides threshold conditions on determining the uniform persistence and extinction of the disease, and predator density at any time should keep larger or equal to its equilibrium level for successful disease eradication. Finally, taking the predation rate as parameter, we provide numerical simulations for the impact of predators on vector-host disease control. It is illustrated that predators have a considerable influence on disease suppression by reducing the density of the vector population.

MSC:

92D30 Epidemiology
92-10 Mathematical modeling or simulation for problems pertaining to biology
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Scholthof, K. G.; Adkins, S.; Czosnek, H.; Palukaitis, P.; Jacquot, E.; Hohn, T.; Hohn, B.; Saunders, K.; Candresse, T.; Ahlquist, P.; Hemenway, C.; Foster, G. D., Top 10 plant viruses in molecular plant pathology, Molecular Plant Pathology, 12, 9, 938-954 (2011)
[2] Giblin-Davis, R. M., Interactions of Nematodes with Insects, Nematode Interactions (1993), London, UK: Chapman and Hall, London, UK
[3] Hemingway, J.; Ranson, H., Insecticide resistance in insect vectors of human disease, Annual Review of Entomology, 45, 371-391 (2000)
[4] Gubler, D. J., Dengue and dengue hemorrhagic fever, Clinical Microbiology Reviews, 11, 3, 480-496 (1998)
[5] Handler, A. M.; James, A. A., Insect Transgenesis: Methods and Applications (2000), Boca Raton, Fla, USA: CRC Press, Boca Raton, Fla, USA
[6] McMeniman, C. J.; Lane, R. V.; Cass, B. N.; Fong, A. W. C.; Sidhu, M.; Wang, Y.; O’Neill, S. L., Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegypti, Science, 323, 5910, 141-144 (2009)
[7] Jeger, M. J.; Holt, J.; van den Bosch, F.; Madden, L. V., Epidemiology of insect-transmitted plant viruses: Modelling disease dynamics and control interventions, Physiological Entomology, 29, 3, 291-304 (2004)
[8] Otim, M.; Legg, J.; Kyamanywa, S.; Polaszek, A.; Gerling, D., Population dynamics of Bemisia tabaci (Homoptera: Aleyrodidae) parasitoids on cassava mosaic disease-resistant and susceptible varieties, Biocontrol Science and Technology, 16, 2, 205-214 (2006)
[9] Zhang, L.; Liu, J.; Wu, H., The screening virulent strain of Beauveria bassiana to Monochamus alternatus, Journal of Nanjing Forestry Unversity, 24, 33-37 (2000)
[10] Lai, Y. X.; Liu, J. D.; Xu, Q. Y.; Wang, Y. H.; Zhou, C. M., Trials on the parasitism of Beauveria bassiana or Verticillium lecanii on larvae of Monochamus alternatus Hope, Journal of Jiangsu University of Science and Technology, 30, 4, 7-9 (2003)
[11] Kaaya, G. P.; Hassan, S., Entomogenous fungi as promising biopesticides for tick control, Experimental and Applied Acarology, 24, 12, 913-926 (2000)
[12] Scholte, E.-J.; Ng’Habi, K.; Kihonda, J.; Takken, W.; Paaijmans, K.; Abdulla, S.; Killeen, G. F.; Knols, B. G. J., An entomopathogenic fungus for control of adult African malaria mosquitoes, Science, 308, 5728, 1641-1642 (2005)
[13] Jenkins, D. W., Pathogens, parasites and predators of medically important arthropods. Annotated list and bibliography, Bulletin of the World Health Organization, 30, 1-150 (1964)
[14] Legner, E., Biological control of diptera of medical and veterinary importance, Journal of Vector Ecology, 20, 59-120 (1995)
[15] Stauffer, J. R.; Arnegard, M. E.; Cetron, M.; Sullivan, J. J.; Chitsulo, L. A.; Turner, G. F.; Chiotha, S.; McKaye, K. R., Controlling vectors and hosts of parasitic diseases using fishes, BioScience, 47, 1, 41-49 (1997)
[16] Samish, M.; Rehacek, J., Pathogens and predators of ticks and their potential in biological control, Annual Review of Entomology, 44, 159-182 (1999)
[17] Kumar, R.; Hwang, J. S., Larvicidal efficiency of aquatic predators: a perspective for mosquito biocontrol, Zoological Studies, 45, 4, 447-466 (2006)
[18] Ostfeld, R. S.; Price, A.; Hornbostel, V. L.; Benjamin, M. A.; Keesing, F., Controlling ticks and tick-borne zoonoses with biological and chemical agents, BioScience, 56, 5, 383-394 (2006)
[19] Walker, K.; Lynch, M., Contributions of Anopheles larval control to malaria suppression in tropical Africa: review of achievements and potential, Medical and Veterinary Entomology, 21, 1, 2-21 (2007)
[20] Nelson, X. J.; Jackson, R. R., A predator from East Africa that chooses malaria vectors as preferred prey, PLoS ONE, 1, 1, article e132 (2006)
[21] Kay, B.; Nam, V. S., New strategy against Aedes aegypti in Vietnam, The Lancet, 365, 9459, 613-617 (2005)
[22] Kittayapong, P.; Yoksan, S.; Chansang, U.; Chansang, C.; Bhumiratana, A., Suppression of dengue transmission by application of integrated vector control strategies at sero-positive GIS-based foci, The American Journal of Tropical Medicine and Hygiene, 78, 1, 70-76 (2008)
[23] Ghosh, S. K.; Tiwari, S. N.; Sathyanarayan, T. S.; Sampath, T. R. R.; Sharma, V. P.; Nanda, N.; Joshi, H.; Adak, T.; Subbarao, S. K., Larvivorous fish in wells target the malaria vector sibling species of the Anopheles culicifacies complex in villages in Karnataka, India, Transactions of the Royal Society of Tropical Medicine and Hygiene, 99, 2, 101-105 (2005)
[24] Ghosh, S. K.; Dash, A. P., Larvivorous fish against malaria vectors: a new outlook, Transactions of the Royal Society of Tropical Medicine and Hygiene, 101, 11, 1063-1064 (2007)
[25] Ross, R., An application of the theory of probabilities to the study of a priori pathometry, Proceedings of the Royal Society of London Series A, 92, 638, 204-230 (1916)
[26] Lashari, A. A.; Zaman, G., Global dynamics of vector-borne diseases with horizontal transmission in host population, Computers & Mathematics with Applications, 61, 4, 745-754 (2011) · Zbl 1217.34064
[27] Wei, H.; Li, X.; Martcheva, M., An epidemic model of a vector-borne disease with direct transmission and time delay, Journal of Mathematical Analysis and Applications, 342, 2, 895-908 (2008) · Zbl 1146.34059
[28] Cai, L.; Li, X., Analysis of a simple vector-host epidemic model with direct transmission, Discrete Dynamics in Nature and Society, 2010 (2010) · Zbl 1190.92029
[29] Luck, R. F.; Shepard, B. M.; Kenmore, P. E., Experimental methods for evaluating arthropod natural enemies, Annual Review of Entomology, 33, 367-389 (1988)
[30] Zehnder, G.; Gurr, G. M.; Kühne, S.; Wade, M. R.; Wratten, S. D.; Wyss, E., Arthropod pest management in organic crops, Annual Review of Entomology, 52, 57-80 (2007)
[31] Srinivasu, P. D. N.; Prasad, B. S. R., Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pest management and biological conservation, Bulletin of Mathematical Biology, 73, 10, 2249-2276 (2011) · Zbl 1334.92369
[32] Bhattacharyya, S.; Bhattacharya, D. K., Pest control through viral disease: mathematical modeling and analysis, Journal of Theoretical Biology, 238, 1, 177-197 (2006)
[33] Moore, S. M.; Borer, E. T.; Hosseini, P. R., Predators indirectly control vector-borne disease: linking predator-prey and host-pathogen models, Journal of the Royal Society Interface, 7, 42, 161-176 (2009)
[34] Okamoto, K. W.; Amarasekare, P., The biological control of disease vectors, Journal of Theoretical Biology, 309, 47-57 (2012) · Zbl 1411.92284
[35] Zhou, F. Y.; Yao, H. X., Dynamics and biocontrol: the indirect effects of a predator population on a host-vector disease model, Abstract and Applied Analysis, 2014 (2014) · Zbl 1406.92646
[36] Diekmann, O.; Heesterbeek, J. A. P.; Metz, J. A. J., On the definition and the computation of the basic reproduction ratio R\sb0 in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28, 4, 365-382 (1990) · Zbl 0726.92018
[37] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48 (2002) · Zbl 1015.92036
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.