Math. Model. Nat. Phenom.
Volume 15, 2020
Mathematical Models and Methods in Epidemiology
|Number of page(s)||43|
|Published online||03 December 2020|
Modeling the effect of temperature variability on malaria control strategies
Department of Mathematics and Applied Mathematics, University of Pretoria,
Pretoria 0002, South Africa.
* Corresponding author: Salisu.Garba@up.ac.za
Accepted: 1 November 2020
In this study, a non-autonomous (temperature dependent) and autonomous (temperature independent) models for the transmission dynamics of malaria in a population are designed and rigorously analysed. The models are used to assess the impact of temperature changes on various control strategies. The autonomous model is shown to exhibit the phenomenon of backward bifurcation, where an asymptotically-stable disease-free equilibrium (DFE) co-exists with an asymptotically-stable endemic equilibrium when the associated reproduction number is less than unity. This phenomenon is shown to arise due to the presence of imperfect vaccines and disease-induced mortality rate. Threshold quantities (such as the basic offspring number, vaccination and host type reproduction numbers) and their interpretations for the models are presented. Conditions for local asymptotic stability of the disease-free solutions are computed. Sensitivity analysis using temperature data obtained from Kwazulu Natal Province of South Africa [K. Okuneye and A.B. Gumel. Mathematical Biosciences 287 (2017) 72–92] is used to assess the parameters that have the most influence on malaria transmission. The effect of various control strategies (bed nets, adulticides and vaccination) were assessed via numerical simulations.
Mathematics Subject Classification: 37C75 / 92D30
Key words: Malaria / vector control / sensitivity analysis / offspring number / reproduction ratio
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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