1. bookVolume 17 (2020): Issue 1 (June 2020)
Journal Details
License
Format
Journal
eISSN
2668-4217
First Published
30 Jul 2019
Publication timeframe
2 times per year
Languages
English
access type Open Access

Analysis of Ode Models for Malaria Propagation

Published Online: 26 May 2020
Volume & Issue: Volume 17 (2020) - Issue 1 (June 2020)
Page range: 31 - 39
Journal Details
License
Format
Journal
eISSN
2668-4217
First Published
30 Jul 2019
Publication timeframe
2 times per year
Languages
English
Abstract

Epidemiological models play an important role in the study of diseases. These models belong to population dynamics models and can be characterized with differential equations. In this paper we focus our attention on two epidemic models for malaria spreading, namely Ross-, and extended Ross model. As both the continous and the corresponding numerical models should preserve the basic qualitative properties of the phenomenon, we paid special attention to its examination, and proved their invariance with reference to the data set. Moreover, existence and uniqueness of equilibrium points for both models of malaria are considered. We demonstrate the theoritical results with numerical simulations.

Keywords

[1] Blanford, J. I., Blanford, S., Crane, R. G., Mann, M. E., Paaijmans, K. P., Schreiber, K. V. and Thomas, M. B., (2013), Implications of temperature variation for malaria parasite development across Africa, doi: 10.1038/srep01300.10.1038/srep01300Search in Google Scholar

[2] Shapiro, L. L. M., Whitehead, S. A. and Thomas, M. B., Quantifying the effects of temperature on mosquito and parasite traits that determine the transmission potential of human malaria, doi: 10.1371/journal.pbio.2003489.10.1371/journal.pbio.2003489Search in Google Scholar

[3] Olaniyi, S. and Obabiyi, O. S. (2013), Mathematical Model for Malaria Transmission Dynamics in Human And Mosquito Populations With Nonlinear Forces of Infection, International Journal of Pure and Applied Mathematics, 88 No.1, pp. 125-156, doi:10.12732/ijpam. v88i1.10.Search in Google Scholar

[4] Ross, R., (1911), The Prevention of Malaria. John Murray, London.Search in Google Scholar

[5] Chitnis, N., Hyman, J. M., and Manore, C.A., (2013), Modelling vertical transmission in vector-borne diseases with applications to Rift Valley fever, Biological Dynamics, 7, pp. 11-40, doi: 10.1080/17513756.2012.733427.Search in Google Scholar

[6] Lashari, A.A., Aly, S., Hattaf, K., Zaman, G., Jung, I.H. and and X. Li (2012), Presentation of Malaria Epidemics Using Multiple Optimal Controls, Journal of Applied Mathematics, 17, doi: 10.1155/2012/946504.10.1155/2012/946504Search in Google Scholar

[7] Labadin, J., C. Kon, M.L. and Juan, S. F. S., (2009), Deterministic malaria transmission model with acquired immunity, Proceedings of the world Congress on Engineering and Computer Science, II, pp. 1-6.Search in Google Scholar

[8] Grant, C.P., Theory of Ordinary Differential Equations, Brigham Young University.Search in Google Scholar

[9] van den Driessche, P., Watmough, J. (2001), Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Canada10.1016/S0025-5564(02)00108-6Search in Google Scholar

[10] Diekmann, O., Heesterbeek, J. A. P. and Metz, J. A. J. (1990), On the de nition and thecomputation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, Mathematical Biology, 28, pp. 365-382.Search in Google Scholar

[11] Mandal, S., Sarkar, R. R. and Sinha, S. (2011), Mathematical models of malaria - a review, Malaria Journal, 10:20210.1186/1475-2875-10-202316258821777413Search in Google Scholar

[12] Capasso, V. (1993), Mathematical Structures of Epidemic Systems, Springer.10.1007/978-3-540-70514-7Search in Google Scholar

[13] Faragó, I., Mincsovics, M. and Mosleh, R. (2018), Reliable numerical modelling of malaria propagation, Application of Mathematics, Springer, 63, No.3, pp. 259-271, doi:10.21136/AM.2018.0098-18.10.21136/AM.2018.0098-18Search in Google Scholar

[14] Faragó, I. and Dorner, F. (2019), Two Epidemic Propagation Models and Their Properties, Lecture Notes in Computer Science, Springer.10.1007/978-3-030-55347-0_18Search in Google Scholar

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