Marcati, Pierangelo; Pozio, M. Assunta Global asymptotic stability for a vector disease model with spatial spread. (English) Zbl 0419.92013 J. Math. Biol. 9, 179-187 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 24 Documents MSC: 92D25 Population dynamics (general) 35R10 Partial functional-differential equations 34K20 Stability theory of functional-differential equations 34K30 Functional-differential equations in abstract spaces 47J25 Iterative procedures involving nonlinear operators 45K05 Integro-partial differential equations 45M10 Stability theory for integral equations 47H20 Semigroups of nonlinear operators Keywords:spread of malaria; vector disease model; asymptotic stability; partial delay differential equation; contracting convexes PDFBibTeX XMLCite \textit{P. Marcati} and \textit{M. A. Pozio}, J. Math. Biol. 9, 179--187 (1980; Zbl 0419.92013) Full Text: DOI References: [1] Busenberg, S., Cooke, K. L.: Periodic Solutions for a Vector Disease Model, in press (1980) [2] Cooke, K. L.: Stability Analysis for a Vector Disease Model, Rocky Mountain J. Math. 9, 31-42 (1979) · Zbl 0423.92029 · doi:10.1216/RMJ-1979-9-1-31 [3] Friedman, A.: Partial Differential Equations. New York: Holt, Reinehart and Wiston, 1969 · Zbl 0224.35002 [4] Hale, J. K.: Theory of Functional Differential Equations. Applied Math. Sciences, Volume 3, New York: Springer-Verlag, 1977 · Zbl 0352.34001 [5] Hoppensteadt, F.: Mathematical Theories of Populations: Demographics, Genetics and Epidemics. SIAM, Philadelphia (1975) · Zbl 0304.92012 [6] La Salle, J.: The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1976) [7] Macdonald, G.: The Epidemiology and Control of Malaria. London: Oxford University Press, 1957 [8] Pogorzelski, W.: Integral Equations and their Applications. London-Warsawa: Pergamon Press-Polish Scientific Publishers, 1966 · Zbl 0137.30502 [9] Pozio, M. A.: Behaviour of Solutions of Some Abstract Functional Differential Equations and Applications to Predator-Prey Dynamics, to appear on Nonlinear Analysis, Theory, Methods and Applications, in press (1980) · Zbl 0444.34063 [10] Protter, M. H., Weinberger, H. F.: Maximum Principles in Differential Equations. Prentice Hall, 1967 · Zbl 0153.13602 [11] Waltman, P.: Deterministic Threshold Models in the Theory of Epidemics. Lecture Notes in Biomathematics 1, Berlin-Heidelberg-New York: Springer-Verlag, 1974 · Zbl 0293.92015 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.