Modelling the Influence of Dynamic Social Processes on COVID-19 Infection Dynamics

Farai Nyabadza (), Josiah Mushanyu, Rachel Mbogo and Gift Muchatibaya
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Farai Nyabadza: Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
Josiah Mushanyu: Department of Computing, Mathematical, and Statistical Science, University of Namibia, Windhoek 13301, Namibia
Rachel Mbogo: Institute of Mathematical Sciences, Strathmore University, P.O. Box 59857, Nairobi 00200, Kenya
Gift Muchatibaya: Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare P.O. Box MP167, Zimbabwe

Mathematics, 2023, vol. 11, issue 4, 1-17

Abstract: Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread, especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave had subsequent waves of COVID-19 infections. In this study, we develop a deterministic model for COVID-19 that includes dynamic non-pharmaceutical interventions known as social dynamics with the goal of simulating the effects of dynamic social processes. The model steady states are determined and their stabilities analysed. The model has a disease-free equilibrium point that is locally asymptotically stable if R 0 < 1 . The model exhibits a backward bifurcation, implying that reducing the reproduction number below one is not sufficient for the elimination of the disease. To ascertain the range of parameters that affect social dynamics, numerical simulations are conducted. The only wave in South Africa in which interventions were purely based on human behavior was the first wave. The model is thus fitted to COVID-19 data on the first wave in South Africa, and the findings given in this research have implications for the trajectory of the pandemic in the presence of evolving societal processes. The model presented has the potential to impact how social processes can be modelled in other infectious disease models.

Keywords: COVID-19; mathematical modelling; stability; dynamic social processes; backward bifurcation; simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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