A co-infection model on TB - COVID-19 with optimal control and sensitivity analysis

COVID-19 had been declared a public health emergency by the World Health Organization in the early 2020. Since then, this deadly virus has claimed millions of lives worldwide. Amidst its chaotic spread, several other diseases have faced negligence in terms of treatment and care, of which one such chronic disease is Tuberculosis. Due to huge rise in COVID-19 cases, there had been a drastic decrease in notification of TB cases which resulted in reversal of global TB target progress. Apart from these due to the earlier co-infections of TB with SARS and MERS-CoV viruses, the TB-COVID-19 co-infection posed a severe threat in the spread of the disease. All these factors backed to be major motivation factor in development of this model. Leading with this concern, a TB - COVID-19 co-infection model is developed in this study, considering possibility of waning immunity of both diseases. Considering different epidemiological traits, an epidemiological model with 11 compartments is developed and the co-dynamics is analysed. A detailed stability and bifurcation analysis is performed for the TB only sub-model, COVID-19 only sub-model and the complete TB - COVID-19 model. Impact of key parameters namely, infection rate, waning immunity, and face mask efficacy on disease prevalence is discussed in detail. Sensitivity analysis by means of normalized forward sensitivity index of the basic reproduction number and LHS-PRCC approach is carried to provide a thorough understanding of significance of various parameters in accelerating as well as controlling the disease spread. Optimal control analysis is presented extensively, incorporating controls related to timely and improved TB treatment, and enhanced COVID-19 tests and isolation facilities to curb the spread of these infectious diseases. The simulation results obtained from each of these analyses stress on the importance of different control measures in mitigation of the diseases and are illustrated accordingly. The study suggests that in the times of a pandemic, other disease treatment and care must not be neglected, and adequate care must be taken so that mortality due to co-infection and unavailability of timely treatment can be avoided.