Stability and control in a stochastic model of malaria population dynamics

• Published in: Advances in continuous and discrete models Vol. 2023; no. 1; p. 45
• Main Authors: Witbooi, Peter J., Maku Vyambwera, Sibaliwe, van Schalkwyk, Garth J., Muller, Grant E.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 15.11.2023; Springer Nature B.V
• Subjects: Analysis; Birth rate; Control stability; Control theory; Dengue fever; Difference and Functional Equations; Differential equations; Dynamic stability; Equilibrium; Functional Analysis; Infections; Malaria; Mathematics; Mathematics and Statistics; Mortality; Mosquitoes; Optimal control; Ordinary Differential Equations; Partial Differential Equations; Pathogens; Per capita; Stochastic models; Theorems; Tropical diseases; SDE model; Basic reproduction number; 92D30; Malaria; Elimination; 34H05; Exponential stability; 34K20
• ISSN: 2731-4235; 1687-1839; 2731-4235; 1687-1847
• DOI: 10.1186/s13662-023-03791-3

This article proves a stability theorem for the disease-free equilibrium of a stochastic differential equations model of malaria disease dynamics. The theorem is formulated in terms of an invariant which is similar to the basic reproduction number of a related deterministic model. Compared to the deterministic model, stability of the disease-free equilibrium holds more generally for the stochastic model. The optimal control theory is applied to the stochastic model, revealing some important new insights. Theoretical results are illustrated by way of simulations.