Vector Epidemic Model of Malaria with Nonconstant-Size Population

Authors

  • Serigne Modou Ndiaye Saint Petersburg State University

DOI:

https://doi.org/10.21638/11701/spbu31.2022.15

Abstract

The paper presents the dynamic characteristics of a vector-host epidemic model with direct transmission. The malaria propagation model is defined by a system of ordinary differential equations. The host population is divided into four subpopulations: susceptible, exposed, infected and recovered, and the vector population is divided into three subpopulations: susceptible, exposed and infected. Using the theory of the Lyapunov functions, certain sufficient conditions for the global stability of the disease-free equilibrium and endemic equilibrium are obtained. The basic reproduction number that characterizes the evolution of the epidemic in the population was found. Finally, numerical simulations are carried out to study the influence of the key parameters on the spread of vector-borne disease.

Keywords:

malaria, mathematical modeling of epidemics, mosquito population, subpopulations, reproductive number, endemic equilibrium

Downloads

Download data is not yet available.
 

References

Baygents, G. and Bani-Yaghoub, M. (2017). A mathematical model to analyze spread of hemorrhagic disease in white-tailed deer population. Journal of Applied Mathematics and Physics, 5, 2262–2282

Cai, L., Tuncer, N. and Martcheva, M. (2017). How does within-host dynamics affect population-level dynamics? Insights from an immuno-epidemiological model of malaria. Mathematical Methods in the Applied Sciences, 40(18), 6424–6450

Diekmann, O., Heesterbeek, A. P. and Roberts, M. G. (2010). The construction of next-generation matrices for compartmental epidemic models. J. R. Soc.Interface, 7, 873–885

Ghosha, M., Lasharib, A. A. and Li, X.-Z. (2013). Biological control of malaria: A mathematical model. Applied mathematics and computation, 219(15), 7923–7939

Gurarie, D., Karl, S., Zimmerman, P. A., King, C. H., St. Pierre, T. G. and Davis, T. M. E. (2012). Dynamical mathematical modeling of malaria infection with innate and adaptive immunity in individuals and agent-based communities. PLoS ONE, 7(3): e34040

Jones, J. H. (2007). Notes on R0. Department of Anthropological Sciences. Stanford, CA, USA, https://web.stanford.edu/jhj1/teachingdocs/Jones-on-R0.pdf (accessed 01.11.2022)

Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A, 115, 700–721

Maliki, O., Romanus, N. and Onyemegbulem, B. (2018). A mathematical modelling of the effect of treatment in the control of malaria in a population with infected immigrants. Applied Mathematics, 9, 1238–1257

Macdonald, G. (1957). The epidemiology and control of malaria. London, New York: Oxford University Press

Mandal, S., Sarkar, R. R. and Sinha, S. (2011). Mathematical models of malaria - a review. Malaria Journal, 10, art. no. 202

Martens, W. J., Niessen, L. W., Rotmans, J., Jetten, T. H. and McMichael, A. J. (1995). Potential Impact of Global Climate Change on Malaria Risk. Environ Health Perspect, 103(5), 458–464

Ndiaye, S. M. and Parilina, E. M. (2022). An epidemic model of malaria without and with vaccination. Pt 1. A model of malaria without vaccination. Vestnik of Saint Petersburg University. Applied Mathematics.Computer Science. Control Processes, 18(2), 263–277 (in Russian)

Ross, R. (1916). An application of the theory of probabilities to the study of a priori pathometry. - Part I. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 92(638), 204–230

Van den Driessche, P. (2017). Reproduction numbers of infectious disease models. Infect. Dis. Model., 2(3), 288–303

Wei, J., Lashari, A. A., Aly, S., Hattaf, K., Zaman, G., Jung, I. H. and Li, X.-Z. (2012). Presentation of Malaria Epidemics Using Multiple Optimal Controls. Journal of Applied Mathematics, art. no. 946504

Zhang, T., Ibrahim, M. M., Kamran, M. A., Naeem, M., Malik, M., Kim, S. and Jung, I. H. (2020). Impact of Awareness to Control Malaria Disease: A Mathematical Modeling Approach. Complexity, art. no. 8657410

Downloads

Published

2023-01-27

How to Cite

Ndiaye, S. M. (2023). Vector Epidemic Model of Malaria with Nonconstant-Size Population. Contributions to Game Theory and Management, 15, 200–217. https://doi.org/10.21638/11701/spbu31.2022.15

Issue

Section

Articles