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MATHEMATICAL MODELLING OF THE IMPACT OF WANING IMMUNITY AND IMMUNE SYSTEM BOOSTING ON MALARIA TRANSMISSION
Keywords:
malaria, mathematical model, basic reproduction number, asymptotic stability, numerical simulation.DOI:
https://doi.org/10.17654/0972087123019Abstract
A deterministic model is formulated to describe the dynamics of malaria transmission using mosquito population and human population structured by immune status. The variation in mortality of humans and mosquitoes due to causes other than malaria, the infectiousness of recovered humans, the decay of acquired immunity and the immune system boosting are taken into account. The existence of biological meaningful solutions has been analyzed and a single disease-free equilibrium has been identified. The basic reproduction number is expressed in terms of the parameters of the model. The stability of the disease-free equilibrium has been analyzed. We have provided some basic conditions in which the disease dies out or persists. The numerical results showed the impact of immunity decay and immune system boosting on malaria transmission.
Received: July 31, 2023
Accepted: September 26, 2023
References
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
Alemu Geleta Wedajo, Boka Kumsa Bole and Purnachandra Rao Koya, The impact of susceptible human immigrants on the spread and dynamics of malaria transmission, American Journal of Applied Mathematics 6(3) (2018), 117-127.
doi: 10.11648/j.ajam.20180603.13.
Ann Nwankwo and Daniel Okuonghae, Mathematical assessment of the impact of different microclimate conditions on malaria transmission dynamics, Math. Biosci. Eng. 16(3) (2019), 1414-1444.
Daniel Sondaz and Jean-Marie Morvan, Autour du théorème de Cauchy- Lipschitz - Equations différentielles, CAPES, agrégation, École d’ingénieurs, Cépadues, 2017.
A. Ducrot, S. B. Sirima, B. Somé and P. Zongo, A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host, Journal of Biological Dynamics 3(6) (2009), 574-598.
Famane Kambiré, Elisée Gouba, Sadou Tao and Blaise Somé, Mathematical analysis of an immune-structured Chikungunya transmission model, European Journal of Pure and Applied Mathematics 12(4) (2019), 1533-1552.
G. A. Ngwa and W. S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Modelling 32 (2000), 747-763.
Jaan Kiusalaas, Numerical Methods in Engineering with MATLAB, Cambridge University Press, 2005.
J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface 2 (2005), 281-293.
doi: 10.1098/rsif.2005.0042.
Lawrence F. Shampine and Mark W. Reichelt, The MATLAB ODE suit, SIAM J. Sci. Comput. 18(1) (1997), 1-22.
M. V. Barbarossa and G. Röst, Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting, J. Math. Biol. 71 (2015), 1737-1770.
N. Chitnis, J. M. Cushing and J. M. Hyman, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol. 70 (2008), 1272-1296. doi: 10.1007/s11538-008-9299-0.
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365-382.
Pierre Aubry and Bernard-Alex Gaüzère, Paludisme, actualités, mise à jour le 04/12/2017, Diplôme de Médecine Tropicale des Pays de l’Océan Indien, 2017.
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29-48.
R. M. Anderson and R. M. May, Infectious Diseases of Humans, Oxford University, Oxford, 1991.
R. Ross, The Prevention of Malaria, John Murray, London, 1911.
Samson Olaniyi, Dynamics of Zika virus model with nonlinear incidence and optimal control strategies, Applied Mathematics and Information Sciences 12(5) (2018), 969-982.
Steven T. Karris, Numerical Analysis Using MATLAB and Excel, Orchard Publications, 3rd ed., 2007.
Won Young Yang, Wenwu Cao, Tae-Sang Chung and John Morris, Applied Numerical Methods Using Matlab, John Wiley and Sons, Inc., 2005.
World Health Organization, World Malaria Report, 2018.
Y. Lou and X. Q. Zhao, A climate-based malaria transmission model with structured vector population, SIAM J. Appl. Math. 70 (2010), 2023-2044.
Yves Cherruaault, Biomathématique, collection que sais-je? (no 2052), 1983.
Yves Cherruault, Modèles et méthodes mathématiques pour les sciences du vivant, Presse Universitaire de France, Paris, 1998.
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