article · Journal of Biological Dynamics
A deterministic mathematical model explores the simultaneous impact of multiple control strategies on the spread of COVID-19. These interventions include vaccination, general protective measures, home quarantine with treatment, and hospital quarantine with treatment. Mathematical analysis confirms core qualitative features, including the positivity and boundedness of solutions, local stabilities of equilibrium points, and the effective reproduction number. The model demonstrates the presence of backward bifurcation when the effective reproduction number drops below one, indicating that simply lowering the reproduction number below this threshold may not fully eliminate the disease. Numerical simulations and sensitivity analyses using published parameter values identify the transmission rate as the most critical factor requiring control. Combining vaccination, protection measures, and quarantine alongside treatment significantly reduces viral transmission across the wider community.
Understanding how multiple public health interventions interact is vital for managing infectious disease outbreaks. By establishing that backward bifurcation can occur, the research highlights that reducing the reproduction rate below one may not guarantee eradication. Identifying the transmission rate as the most critical factor reinforces the need for strict containment, helping authorities prioritise layered control measures during epidemics.
This theoretical modelling work provides foundational insights that could inform epidemic forecasting software and public health decision-support tools. Potential users include epidemiological researchers, public health planners, and healthcare administrators managing disease response strategies. Because the findings rely on mathematical derivations and numerical simulations using literature-derived parameters, the work represents early-stage research that requires integration into tested policy or clinical workflows before practical deployment.
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The novel Coronavirus (COVID-19) infection has become a global public health issue, and it has been a cause for morbidity and mortality of more people throughout the world. In this paper, we investigated the impacts of vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment strategies simultaneously using a deterministic mathematical modelling approach. No one has considered these intervention strategies simultaneously in his/her modelling approach. We examined all the qualitative properties of the model such as the positivity and boundedness of the model solutions, the disease-free and endemic equilibrium points, the effective reproduction number using next-generation matrix method, local stabilities of equilibrium points using the Routh-Hurwitz method. Using the Centre Manifold criteria, we have shown the existence of backward bifurcation whenever the COVID-19 effective reproduction number is less than unity. Moreover, we have analysed both sensitivity and numerical simulation using parameter values taken from published literature. The numerical results show that the transmission rate is the most sensitive parameter we have to control. Also vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment have great effects to minimize the COVID-19 transmission in the community.
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DOI: 10.1080/17513758.2022.2111469
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