caa a22 4500 445330406 CHVBK 20180317142735.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00285-010-0346-8 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0346-8 A reaction-diffusion malaria model with incubation period in the vector population [Elektronische Daten] [Yijun Lou, Xiao-Qiang Zhao] Malaria is one of the most important parasitic infections in humans and more than two billion people are at risk every year. To understand how the spatial heterogeneity and extrinsic incubation period (EIP) of the parasite within the mosquito affect the dynamics of malaria epidemiology, we propose a nonlocal and time-delayed reaction-diffusion model. We then define the basic reproduction ratio $${\mathcal{R}_0}$$ and show that $${\mathcal{R}_0}$$ serves as a threshold parameter that predicts whether malaria will spread. Furthermore, a sufficient condition is obtained to guarantee that the disease will stabilize at a positive steady state eventually in the case where all the parameters are spatially independent. Numerically, we show that the use of the spatially averaged system may highly underestimate the malaria risk. The spatially heterogeneous framework in this paper can be used to design the spatial allocation of control resources. Springer-Verlag, 2010 Malaria transmission nationallicence Spatial heterogeneity nationallicence Incubation period nationallicence Basic reproduction ratio nationallicence Threshold dynamics nationallicence Global attractivity nationallicence Lou Yijun Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John's, NL, Canada aut Zhao Xiao-Qiang Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John's, NL, Canada aut Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 543-568 0303-6812 62:4<543 2011 62 285 https://doi.org/10.1007/s00285-010-0346-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0346-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lou Yijun Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John's, NL, Canada aut NATIONALLICENCE 700 1- Zhao Xiao-Qiang Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7, St. John's, NL, Canada aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/4(2011-04-01), 543-568 0303-6812 62:4<543 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer