Эпидемическая модель малярии без вакцинации и при ее наличии. Ч. 1. Модель малярии без вакцинации

Serine Modou Ndiaye; Elena M. Parilina

doi:10.21638/11701/spbu10.2022.207

Authors

Serine Modou Ndiaye St. Petersburg State University, 199034, St. Petersburg, Russian Federation
Elena M. Parilina St. Petersburg State University, 199034, St. Petersburg, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2022.207

Abstract

We propose a mathematical model of the malaria epidemic in the human population (host), where the transmission of the disease is produced by a vector population (mosquito) known as the malaria mosquito. The malaria epidemic model is defined by a system of ordinary differential equations. The host population at any time is divided into four sub-populations: susceptible, exposed, infectious, recovered. Sufficient conditions for stability of equilibrium without disease and endemic equilibrium are obtained using the Lyapunov’s function theory. We define the reproductive number characterizing the level of disease spreading in the human population. Numerical modeling is made to study the influence of parameters on the spread of vector-borne disease and to illustrate theoretical results, as well as to analyze possible behavioral scenarios.

Keywords:

epidemic model, human population, malaria, sub-populations, modification epidemic SEIR model, reproductive number, endemic equilibrium

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References

Литература

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Ndiaye S. M., Lam M., Mansal F. Modélisation d’un système de pêcherie avec maladie. Bachelor Thesis, 2017, pp. 3–10.

Aldila D., Seno H. A. Population dynamics model of mosquito-borne disease transmission, focusing on mosquitoes’ biased distribution and mosquito repellent use. Bull. Math. Biol., 2019, vol. 81, pp. 4977–5008.

Lipsitch M., Cohen T., Cooper B., Robins J. M., Ma S., James L., Gopalakrishna G., Chew S. K., Tan C. C., Samore M. H., Fisman D., Murray M. Transmission dynamics and control of severe acute respiratory syndrome. Science, 2003, vol. 300, pp. 1966–1970.

Britton T. Stochastic epidemic models: A survey. Mathematical Biosciences, 2010, vol. 225, iss. 1, pp. 24–35.

Lashari A. A., Zaman G. Global dynamics of vector-borne diseases with horizontal transmission in host population. Computers & Mathematics with Applications, 2011, vol. 61, iss. 4, pp. 745–754.

Arquam M., Anurag S., Cherifi H. Impact of seasonal conditions on vector-borne epidemiological dynamics. IEEE Access, 2020, vol. 8, pp. 94510–94525.

Kim M., Paini D., Jurdak R. Modeling stochastic processes in disease spread across a heterogeneous social system. Proceedings of the National Academy of Sciences, 2019, vol. 116, no. 2, pp. 401–406.

Derdei B. Étude de modèles épidémiologiques: Stabilité, observation et estimation de paramètres. HAL theses, 2013, pp. 7–11. Available at: https://tel.archives-ouvertes.fr/tel-00841444/file/BicharaPhDThesis.pdf (accessed: April 15, 2022).

Hyman J. M., Li J. An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations. Mathematical Biosciences, 2000, vol. 167, no. 1, pp. 65–86.