Alladi Ramakrishnan Hall

Mathematical Modeling of COVID-19

Shraddha Bandekar

Vellore Institute of Technology, Chennai

Studying the COVID-19 dynamics by means of various mathematical models is a bit elusive but is a significant tool towards estimation and prediction of the pandemic outbreak. The research problem directs towards developing and analysing different mathematical models which adheres closest with the real-life scenario justifying the COVID-19 disease spread and presenting interventions accordingly. In the first work, we developed a deterministic model incorporating detected and undetected infectives with inclusion of face-mask efficacy and provided a detailed analysis of the model with data fitting and short-term predictions for the country India and its worst hit states along with optimal control analysis. We next formulate a COVID-19 epidemiological model applying media information factor by means of Holling Type-II function. Optimal control analysis is performed by applying controls related to social distancing, detection, and treatment facilities. A comparison is provided for the countries of India and Nepal. Sensitivity analysis in terms of PRCC is provided in detail in this study. We then framed models considering limited availability of medical resources, one with natural demography and inclusion of face mask efficacy, and the other with lockdown impact for different phases of lockdown. In both these models, treatment function is framed, wherein the difference is in terms of the model formulation and treatment function defined. In the former study, with crossing of threshold value, a constant number of in infectives get treatment, whereas in the latter there is gradual decrease which ultimately reaches a saturation value. Detailed mathematical analysis in terms of stability analysis, sensitivity of the basic reproduction number, prevalence and data fitting is presented. The latter is also extended to stochastic model to study the randomness in treatment and removed classes. In each of these four models, parameter estimation is done, and results are explained accordingly. The study is concluded with a TB – COVID-19 co-infection model aimed at studying the impact of one over other as well suggesting intervention strategies for mitigation of the diseases and controlling co-infection. Numerical simulation and control analysis suggests that if adequate TB care is not provided and awareness is not spread, the disease spread can rise rapidly. In this model, we include waning of immunity as well.