Keywords and phrases: Plasmodium falciparum, model, stochastic differential equations.
Received: August 7, 2023; Revised: October 6, 2023; Accepted: November 22, 2023
How to cite this article: Abdoul Karim DRABO, Frédéric BERE, Sibiri Narcisse DOLEMWEOGO and S. P. Clovis NITIEMA, A stochastic model for the spread of human plasmodia, Advances in Differential Equations and Control Processes 30(4) (2023), 363-383. http://dx.doi.org/10.17654/0974324323020
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References: [1] Ronald Ross, The Prevention of Malaria, John Murray, London, 1911. [2] David L. Smith, Katherine E. Battle, Simon I. Hay, Christopher M. Barker, Thomas W. Scott and F. Ellis McKenzie, Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens, PLoS Pathogens 8(4) (2012), e1002588. [3] Rachel Waema Mbogo, Livingstone S. Luboobi and John W. Odhiambo, A stochastic model for malaria transmission dynamics, J. Appl. Math. 2018 (2018), Art. ID 2439520, 13 pp. [4] Reuben I. Gweryina and Anande R. Kimbir, Dynamical behavior of a malaria relapse model with insecticide treated nets (itns) as protection measure, Applications and Applied Mathematics: An International Journal (AAM) 15(1) (2020), 9. [5] Yongli Cai, Yun Kang and Weiming Wang, A stochastic SIRS epidemic model with nonlinear incidence rate, Appl. Math. Comput. 305 (2017), 221-240. [6] Xiaomei Ren and Tiansi Zhang, Global analysis of an SEIR epidemic model with a ratio dependent nonlinear incidence rate, Journal of Applied Mathematics and Physics 5(12) (2017), 2311-2319. [7] Derdei Bichara, Etude de modèles épidémiologiques: stabilité, observation et estimation de paramètres, PhD thesis, Université de Lorraine, 2013. [8] Pauline van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180(1-2) (2002), 29-48. [9] Julie Mintsa Mi Ondo Mintsa Mi Ondo, Les aspects spatiaux dans la modélisation en épidémiologie, PhD thesis, Université de Grenoble, 2012. [10] Jacek Banasiak, Rachid Ouifki and Woldegebriel Assefa Woldegerima, Some mathematical tools for modelling malaria: a subjective survey, Biomath 10 (2021), 1-19. [11] Francis Mugabi, Kevin J. Duffy, Joseph Y. T. Mugisha and Obiora C. Collins, Determining the effects of transplacental and direct transmission on the probability of persistence in a bluetongue virus model in temperate and tropical regions, Results in Applied Mathematics 7 (2020), 100120. [12] Gideon A. Ngwa and William S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Modelling 32(7-8) (2000), 747-763. [13] R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1973. [14] X. R. Mao, Stochastic Differential Equations and their Applications, Horwood Publishing House, Chichester, 1997.
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