Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment

Abstract

In this study, we propose an HIV-TB co-infection model by considering the treatment provision limitation induced by recent COVID-19 pandemic that impacts this dual epidemic immensely, assimilating the significance of educational attempts. We analyze the model and its submodels with single infections individually. We obtain the awareness-induced basic reproduction numbers and discuss the global stability of disease-free equilibrium when provision limitation is zero. We observe that the submodels exhibit forward as well as backward bifurcations under provision restriction. Further, we derive thresholds for resource limitations regulating the dynamical behavior of the systems while analyzing the stability of endemic equilibrium of the models with single infections. Sophisticated simulation approaches are implemented to discover the influences of provision-restricted medication and awareness on dual epidemic. Our findings convey the persistence of co-infection though the basic reproduction number is below unity, if the provision restriction remains uncurbed. An observable insight is that, in spite of having epidemic threshold less than unity and no limitation in TB treatment, co-infection relapses and persists in the population, when there is no awareness attempt. Numerical findings emphasize the urgent need of increased treatment accessibility and importance of awareness in the current situation. Moreover, an optimization problem incorporating treatment and awareness controls is formulated and solved to find the ideal strategy to manage HIV-TB co-epidemic that recommends to diminish the medical resource limitation to get the enormous impact in dominating the adversity caused by COVID-19.

Effect of awareness, quarantine and vaccination as control strategies on COVID-19 with Co-morbidity and Re-infection

“…Quadratic objective functional is considered due to the fact that intervention is non-linear in its nature ( Ndii and Adi, 2021 ). In fact, quadratic control is a common form of an objective functional in an optimal control problem and is frequently used in the literature ( Ndii and Adi, 2021 , Alemneh and Alemu, 2021 , Kim et al., 2018 , Shen et al., 2021 , Majumder et al., 2022 , Zamir et al., 2021 , Omame et al., 2020 , Li and Guo, 2022 ). Thus we have the following objective functional …”

Systematic description of COVID-19 pandemic using exact SIR solutions and Gumbel distributions

“…More recent studies on the mathematical modeling of the COVID-19 pandemic can be found in the Refs. [ 33 – 39 ].…”

Systematic description of COVID -19 pandemic using exact SIR solutions and Gumbel distributions

“…More recent studies on the mathematical modeling of the COVID-19 pandemic can be found in the Refs. [33][34][35][36][37][38][39].…”