zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A schistosomiasis model with mating structure and time delay. (English) Zbl 1130.92051
Summary: A system of homogeneous equations with a time delay is used to model the population dynamics of schistosomes. The model includes the parasite’s mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasite’s life cycle. Invasion criteria of resistant strains and coexistence threshold conditions are derived. These results are used to explore the impact of drug treatment on resistant strain survival. Numerical simulations indicate that the dynamical behaviors of the current model are not qualitatively different from those derived from an earlier model that ignores the impact of time delays associated with the multiple stages in the parasite’s life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.
MSC:
92D40Ecology
34K60Qualitative investigation and simulation of models
References:
[1]Basch, P. F.: Schistosomes, development, reproduction, and host relations, (1991)
[2]Castillo-Chavez, C.; Huang, W.; Li, J.: On the existence of stable pairing distributions, J. math. Biol. 34, 413 (1996) · Zbl 0840.92017 · doi:10.1007/BF00167942
[3]Castillo-Chavez, C.; Huang, W.; Li, J.: Competitive exclusion and coexistence of multiple strains in an SIS STD model, SIAM J. Appl. math. 59, 1790 (1999) · Zbl 0934.92029 · doi:10.1137/S0036139997325862
[4]CDC, Schistosomiasis fact sheet, 2004. Available from: lt;http://www.cdc.gov/ncidod/dpd/parasites/schistosomiasis/factshtschistosomiasis.htm/gt;.
[5]Cioli, D.: Praziquantel: is there real resistance and are there alternatives?, Curr. opin. Infect. dis. 13, 659 (2000)
[6]Cosgrove, C. L.; Southgate, V. R.: Mating interactions between schistosoma mansoni and S. Margrebowiei, Parasitology 125, 233 (2002)
[7]Fallon, P. G.; Tao, L. -F.; Ismail, M. M.; Bennett, J. L.: Schistosome resistance to praziquantel: fact or artifact?, Parasitol. today 12, 316 320 (1996)
[8]Feng, Z.; Curtis, J.; Minchella, D. J.: The influence of drug treatment on the maintenance of schistosome genetic diversity, J. math. Biol. 43, 52 (2001) · Zbl 0986.92017 · doi:10.1007/s002850100092
[9]Feng, Z.; Eppert, A.; Milner, F. A.; Minchella, D. J.: Estimation of parameters governing the transmission dynamics of schistosomes, Appl. math. Lett. 17, 1105 (2004) · Zbl 1063.92028 · doi:10.1016/j.aml.2004.02.002
[10]K.P. Hadeler, Pair formation in age structured populations, in: A. Kurzhanskij, K. Sigmund (Eds.), Proc. Workshop on Selected Topics in Biomathematics, IIASA, Laxenburg, Austria, Acta Appl. Math. 14 (1989) 91. · Zbl 0667.92013 · doi:10.1007/BF00046676
[11]Hadeler, K. P.: Pair formation models with maturation period, J. math. Biol. 32, 1 (1993) · Zbl 0808.92024 · doi:10.1007/BF00160370
[12]Hadeler, K. P.; Ngoma, K.: Homogeneous models for sexually transmitted diseases, Rocky mountain J. Math. 20, 967 (1990) · Zbl 0733.92020 · doi:10.1216/rmjm/1181073055
[13]Hadeler, K. P.; Waldstatter, R.; Worz-Busekros, A.: Models for pair formation in bisexual populations, J. math. Biol. 26, 635 (1988) · Zbl 0714.92018 · doi:10.1007/BF00276145
[14]Ismail, M.; Botros, S.; Metwally, A.; William, S.; Farghally, A.; Tao, L.; Day, T. A.; Bennett, J. L.: Resistance to praziquantel: direct evidence from schistosoma mansoni isolated from Egyptian villagers, Am. soc. Trop. med. Hyg. 60, 932 (1999)
[15]J.H. Pollard, Mathematical Models for The Growth of Human Populations, Chapter 7: The Two Sex Problem, Cambridge University Press, Cambridge, 1973.
[16]Tchuenté, L. A. Tchuem; Southgate, V. R.; Imbert-Establet, D.; Jourdane, J.: Change of mate and mating competition between males of schistosoma intercalatum and S. Mansoni, Parasitology 110, 45 (1995)
[17]WHO, Schistosomiasis, 2004. Available from: lt;ttp://www.who.int/tdr/dw/schisto2004.htm/gt;.
[18]Xu, D.; Curtis, J.; Feng, Z.; Minchella, D. J.: On the role of schistosome mating structure in the maintenance of drug resistant strains, Bull.math. biol. 67, 1207 (2005)