Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

Abstract

A new mathematical model incorporating epidemiological features of the co-dynamics of tuberculosis (TB) and SARS-CoV-2 is analyzed. Local asymptotic stability of the disease-free and endemic equilibria are shown for the sub-models when the respective reproduction numbers are below unity. Bifurcation analysis is carried out for the TB only sub-model, where it was shown that the sub-model undergoes forward bifurcation. The model is fitted to the cumulative confirmed daily SARS-CoV-2 cases for Indonesia from February 11, 2021 to August 26, 2021. The fitting was carried out using the fmincon optimization toolbox in MATLAB. Relevant parameters in the model are estimated from the fitting. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established through the application of Pontryagin’s Principle. Different control strategies: face-mask usage and SARS-CoV-2 vaccination, TB prevention as well as treatment controls for both diseases are considered. Simulations results show that: (1) the strategy against incident SARS-CoV-2 infection averts about 27,878,840 new TB cases; (2) also, TB prevention and treatment controls could avert 5,397,795 new SARS-CoV-2 cases. (3) In addition, either SARS-CoV-2 or TB only control strategy greatly mitigates a significant number of new co-infection cases.

A model for COVID-19 and bacterial pneumonia coinfection with community- and hospital-acquired infections

“…Although many models have been proposed recently to study the coinfection dynamics of COVID-19 and other diseases [41,42,43,44,45,46], our work is the first that takes into account the distinctive features of bacterial pneumonia, in particular, the inclusion of two infection ways (community and hospital transmission).…”

“…Tuberculosis-COVID-19 coinfection has been modelled by Bandedar and Ghosh [43], who considered a model with waning immunity and performed a bifurcation and stability analysis, as well as simulations using data from India. A different model for tuberculosis coinfection was studied by Rwezaura et al [44], who investigated the effects of COVID-19 vaccination and treatment control and performed parameter fitting with data from Indonesia. Optimal control for a COVID-19-dengue model was studied by Omame et al [45] using five controls; furthermore, the authors fitted their model to the cumulative COVID-19 cases and deaths in Brazil.…”

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

“…For example in the study of Malaria ( Cai, Li, Tuncer, Martcheva, & Lashari, 2017 ; Makinde & Okosun, 2011 ; Mohammed-Awel & Gumel, 2019 ), TB ( Das, Khajanchi, & Kar, 2020 ; Kim, Aurelio, & Jung, 2018 ), COVID-19 ( Lemecha Obsu & Feyissa Balcha, 2020 ; Mondal & Khajanchi, 2022 ), HIV-TB coinfection ( Aggarwal et al., 2020a ; Silva & Torres, 2015 ), Malaria-COVID-19 coinfection ( Tchoumi et al., 2021 ), COVID-19 and Diabetes coinfection ( Omame, Sene, et al., 2021 ) and the references there in. Recently, some mathematical modeling of COVID-19 and TB co-infection with optimal control have been proposed and analyzed ( Goudiaby et al., 2022 ; Mekonen, Obsu, & Habtemichael, 2022 ; Rwezaura, Diagne, Omame, de Espindola, & Tchuenche, 2022 ). In particular, Goudiaby et al.…”

“…They showed that the prevalence of the co-infection reduced when concurrently all the control measures were implemented. On the other hand, Rwezaura et al. (2022) proposed the co-infection model for SARS-CoV-2 and TB that incorporates the vaccinated population with optimal control strategies to manage the spread of these two diseases.…”

“…For example, compared to the model proposed in ( Goudiaby et al., 2022 ; Mekonen et al., 2022 ), our model considers the vaccination against COVID-19, TB re-infection after recovery, and exogenous TB re-infection. Moreover, compared to the model given in ( Rwezaura et al., 2022 ), our model considers the exogenous TB re-infection.…”