Parasite sources and sinks in a patched Ross–Macdonald malaria model with human and mosquito movement: Implications for control

Mathematical Biosciences

Volumn 279, Issue , 2016, Pages 90-101

  Ruktanonchai, Nick W ^a   Smith, David L ^b   De Leenheer, Patrick ^c  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^b UNIVERSITY OF WASHINGTON   (United States)

^c OREGON STATE UNIVERSITY   (United States)

Author keywords

Basic reproduction number; Control; Malaria transmission; Monotone systems; Patched model

Indexed keywords

CONTROL; DISEASES; POPULATION STATISTICS; VECTORS;

BASIC REPRODUCTION NUMBER; CONTROL STRATEGIES; HETEROGENEOUS ENVIRONMENTS; MALARIA TRANSMISSION; MONOTONE SYSTEMS; NATURAL LANDSCAPES; PARASITE POPULATION; STABLE STEADY STATE;

MALARIA CONTROL;

DISEASE CONTROL; DISEASE TRANSMISSION; MALARIA; MODELING; MOSQUITO; PARASITE; PATHOGEN;

ARTICLE; DISEASE TRANSMISSION; ENVIRONMENTAL FACTOR; HOST PARASITE INTERACTION; HUMAN; LANDSCAPE; MALARIA CONTROL; MATHEMATICAL COMPUTING; MOSQUITO; NONHUMAN; PATCHED ROSS MACDONALD MALARIA MODEL; POPULATION DYNAMICS; REPRODUCTION; STATISTICAL MODEL; STEADY STATE; VECTOR CONTROL; ANIMAL; MALARIA; MICROBIOLOGY; MOSQUITO VECTOR; PHYSIOLOGY; THEORETICAL MODEL; TRANSMISSION;

ANIMALS; CULICIDAE; HUMANS; MALARIA; MODELS, THEORETICAL; MOSQUITO VECTORS;

EID: 84979619142     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2016.06.012     Document Type: Article

References (37)

1. [1] Arino, J., van den Driessche, P., A multi-city epidemic model. Math. Popul. Stud. 10 (2003), 175–193.
2. [2] Arino, J., Davis, J.R., Hartley, D., Jordan, R., Miller, J.M., van den Driessche, P., A multi-species epidemic model with spatial dynamics. Math. Med. Biol. 22 (2005), 129–142.
3. [3] Arino, J., Diseases in metapopulations. Ma, Z., Zhou, Y., Wu, J., (eds.) Modeling and Dynamics of Infectious Diseases, 2009, World Scientific, 65–123.
4. [4] Arino, J., Portet, S., Epidemiological implications of mobility between a large urban centre and smaller satellite cities. J. Math. Biol. 71 (2015), 1243–1265.
5. [5] Auger, P., Kouokam, E., Sallet, G., Tchuente, M., Tsanou, B., The Ross–Macdonald model in a patchy environment. Math. Biosci. 216 (2008), 123–131.
6. [6] Bejon, P., Williams, T.N., Nyundo, C., Hay, S.I., Benz, D., Gething, P.W., Otiende, M., Peshu, J., Bashraheil, M., Greenhouse, B., Bousema, T., Bauni, E., Marsh, K., Smith, D.L., Borrmann, S., A micro-epidemiological analysis of febrile malaria in coastal Kenya showing hotspots within hotspots. eLife, 2014, 1–19, 10.7554/eLife.02130.
7. [7] Berman, A., Plemmons, P.J., Nonnegative Matrices in the Mathematical Sciences, 1994, SIAM.
8. [8] Bousema, T., Drakeley, C., Gesase, S., Hashim, R., Magesa, S., Mosha, F., Otieno, S., Carneiro, I., Cox, J., Msuya, E., Kleinschmidt, I., Maxwell, C., Greenwood, B., Riley, E., Sauerwein, R., Chandramohan, D., Gosling, R., Identification of hot spots of malaria transmission for targeted malaria control. J. Infect. Dis. 201 (2010), 1764–1774.
9. [9] Bousema, T., Griffin, J.T., Sauerwein, R.W., Smith, D.L., Churcher, T.S., Takken, W., Ghani, A., Drakeley, C., Gosling, R., Hitting hotspots: spatial targeting of malaria for control and elimination. PLOS Med., 9, 2012, e1001165.
10. [10] http://www.cdc.gov/malaria/about/faqs.html.
11. [11] Cosner, C., Beier, J.C., Cantrell, R.S., Impoinvil, D., Kapitanski, L., Potts, M.D., Troyo, A., Ruan, S., The effects of human movement on the persistence of vector-borne diseases. J. Theor. Biol. 258 (2009), 550–560.
12. [12] Cosner, C., Models for the effects of host movement in vector-borne disease systems. Math. Biosci. 270 (2015), 192–197.
13. [13] van den Driessche, P., Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002), 29–48.
14. [14] Gao, D., Ruan, S., An SIS patch model with variable transmission coefficients. Math. Biosci. 232 (2011), 110–115.
15. [15] Gao, D., Ruan, S., Malaria models with spatial effects. Chen, D., Moulin, B., Wu, J., (eds.) Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases, 2014, John Wiley & Sons, 3–30.
16. [16] Githeko, A.K., Ayisi, J.M., Odada, P.K., Atieli, F.K., Ndenga, B.A., Githure, J.I., Yan, G., Topography and malaria transmission heterogeneity in Western Kenya highlands: prospects for focal vector control. Malaria J., 5, 2006, 107.
17. [17] Hasibeder, G., Dye, C., Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment. Theor. Popul. Biol. 33 (1988), 31–53.
18. [18] Hsieh, Y.-H., van den Driessche, P., Wang, L., Impact of travel between patches for spatial spread of disease. Bull. Math. Biol. 69 (2007), 1355–1375.
19. [19] Killeen, G.F., Knols, B.G.J., Gu, W., Taking malaria transmission out of the bottle: implications of mosquito dispersal for vector-control interventions. Lancet Infect. Dis. 3 (2003), 297–303.
20. [20] Koella, J.C., On the use of mathematical models of malaria transmission. Acta Trop. 49 (1991), 1–25.
21. [21] Lajmanovich, A., Yorke, J.A., A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28 (1976), 221–236.
22. [22] C.A. Manore, K.S. Hickmann, J.M. Hyman, I.M. Foppa, J.K. Davis, D.M. Wesson, C.N. Mores, A Network-Patch Methodology for Adapting Agent-based Models for Directly Transmitted Disease to Mosquito-Borne Disease. arXiv:1405.2258v1.
23. [23] Mbogo, C.M., Mwangangi, J.M., Nzovu, J., Gu, W., Yan, G., Gunter, J.T., Swalm, C., Keating, J., Regens, J.L., Shililu, J.I., Githure, J.I., Beier, J.C., Spatial and temporal heterogeneity of anopheles mosquitoes and Plasmodium falciparum transmission along the Kenyan coast. Am. J. Trop. Med. Hygiene 68 (2003), 734–742.
24. [24] Moonen, B., Cohen, J.M., Snow, R.W., Slutsker, L., Drakeley, C., Smith, D.L., Abeyasinghe, R.R., Rodriguez, M.H., Maharaj, R., Tanner, M., Targett, G., Operation strategies to achieve and maintain malaria elimination. Lancet 376 (2010), 1592–1603.
25. [25] Paull, S.H., Song, S., McClure, K.M., Sackett, L.C., Kilpatrick, A.M., Johnson, P.T.J., From superspreaders to disease hotspots: linking transmission across hosts and space. Front. Ecol. Environ. 10 (2012), 75–82.
26. [26] Prothero, R.M., Disease and mobility: a neglected factor in epidemiology. Int. J. Epidemiol. 6 (1977), 259–267.
27. [27] Prosper, O., Ruktanonchai, N., Martcheva, M., Assessing the role of spatial heterogeneity and human movement in malaria dynamics and control. J. Theor. Biol. 303 (2012), 1–14.
28. [28] Rodriguez, D.J., Torres-Sorando, L., Models of infectious diseases in spatially heterogeneous environments. Bull. Math. Biol. 63 (2001), 547–571.
29. [29] N.W. Ruktanonchai, P. De Leenheer, A.J. Tatem, V.A. Alegana, T.T. Caughlin, E. zu Erbach-Schoenberg, C. Lourenco, C.W. Ruktanonchai, D.L. Smith, Identifying malaria transmission foci for elimination using human mobility data, PLoS Comput. Biol. 12(4) e1004846. doi: 10.1371/journal.pcbi.1004846.
30. [30] Smith, H.L., Monotone Dynamical Systems, 1995, AMS.
31. [31] Smith, D.L., McKenzie, F.E., Statics and dynamics of malaria infection in anopheles mosquitoes. Malaria J., 3, 2004, 13.
32. [32] Smith, D.L., Battle, K.E., Hay, S.I., Barker, C.M., Scott, T.W., McKenzie, F.E., Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathogens, 8, 2012, e1002588.
33. [33] Stoddard, S.T., Morrison, A.C., Vazquez-Prokopec, G.M., Soldan, V.P., Kochel, T.J., Kitron, U., Elder, J.P., Scott, T.W., The role of human movement in the transmission of vector-borne pathogens. PLOS Neglected Trop. Dis., 3, 2009, e481.
34. [34] Tatem, A.J., Smith, D.L., International population movements and regional Plasmodium falciparum malaria elimination strategies. Proc. Natl. Acad. Sci. 107 (2010), 12222–12227.
35. [35] Wang, W., Epidemic models with population dispersal. Takeuchi, Y., Iwasa, Y., Sato, K., (eds.) Mathematics for Life Science and Medicine, 2007, Springer-Verlag, 67–95.
36. [36] Wesolowski, A., Eagle, N., Tatem, A.J., Smith, D.L., Noor, A.M., Snow, R.W., Buckee, C.O., Quantifying the impact of human mobility on malaria. Science 338 (2012), 267–270.
37. [37] Zhuo, G., Munga, S., Minakawa, N., Githeko, A.K., Yan, G., Spatial relationship between adult malaria vector abundance and environmental factors in Western Kenya highlands. Am. J. Trop. Med. Hygiene 77 (2007), 29–35.