In this paper, we discuss a mathematical model of malaria transmission between vector and host population. We study the basic qualitative properties of the model, the boundedness and non-negativity, calculate all equilibria, and prove the global stability of them and the behaviour of the model when the basic reproduction ratio R0 is greater than one or less than one. The global stability of equilibria is established by using Lyapunov method. Graphical representations of the calculated parameters and their effects on disease eradication are provided.
World Health Organization (2023) Malaria Report. https://www.who.int/news-room/fact-sheets/detail/malaria
[3]
Kayentao, K., Ongoiba, A., Preston, A.C., Healy, S.A., Doumbo, S., Doumtabe, D., et al. (2022) Safety and Efficacy of a Monoclonal Antibody against Malaria in Mali. New England Journal of Medicine, 387, 1833-1842. https://doi.org/10.1056/nejmoa2206966
[4]
Wu, R.L. et al. (2022) Low-Dose Subcutaneous or Intravenous Monoclonal Antibody to Prevent Malaria. The New England Journal of Medicine, 387, 397-407.
[5]
Kayentao, K., Ongoiba, A., Preston, A.C., Healy, S.A., Hu, Z., Skinner, J., et al. (2024) Subcutaneous Administration of a Monoclonal Antibody to Prevent Malaria. New England Journal of Medicine, 390, 1549-1559. https://doi.org/10.1056/nejmoa2312775
[6]
(2023) NIAID Media Team, World Mosquito Day 2023—How Mathematical Modeling Reveals the Link between Climate Change and Mosquito-Borne Diseases. https://www.niaid.nih.gov/news-events/world-mosquito-day-2023
[7]
Gardner, M.J., Hall, N., Fung, E., White, O., Berriman, M., Hyman, R.W., et al. (2002) Genome Sequence of the Human Malaria Parasite Plasmodium Falciparum. Nature, 419, 498-511. https://doi.org/10.1038/nature01097
[8]
Mandal, S., Sarkar, R.R. and Sinha, S. (2011) Mathematical Models of Malaria—A Review. Malaria Journal, 10, Article No. 202. https://doi.org/10.1186/1475-2875-10-202
[9]
Ross, R. (1915) Some a Priori Pathometric Equations. BMJ, 1, 546-547. https://doi.org/10.1136/bmj.1.2830.546
[10]
Olutimo, A.L., Mbah, N.U., Abass, F.A. and Adeyanju, A.A. (2024) Effect of Environmental Immunity on Mathematical Modeling of Malaria Transmission between Vector and Host Population. Journal of Applied Sciences and Environmental Management, 28, 205-212. https://doi.org/10.4314/jasem.v28i1.23
[11]
Diekmann, O., Heesterbeek, J.A.P. and Roberts, M.G. (2009) The Construction of Next-Generation Matrices for Compartmental Epidemic Models. Journal of the Royal Society Interface, 7, 873-885. https://doi.org/10.1098/rsif.2009.0386
[12]
Abioye, A.I., Peter, O.J., Oguntolu, F.A., Adebisi, A.F. and Aminu, T.F. (2020) Global Stability of Seir-Sei Model of Malaria Transmission. Advances in Mathematics: Scientific Journal, 9, 5305-5317. https://doi.org/10.37418/amsj.9.8.2
[13]
Barbashin, E.A. (1970) Introduction to the Theory of Stability. Wolters-Noordhoff.
[14]
LaSalle, J.P. (1976) The Stability of Dynamical Systems. SIAM.
[15]
Lyapunov, A.M. (1992) The General Problem of the Stability of Motion. International Journal of Control, 55, 531-534. https://doi.org/10.1080/00207179208934253
