Optimal control analysis of a COVID-19 and tuberculosis co-dynamics model

Burden of COVID-19 pandemic on tuberculosis hospitalisation patterns at a tertiary care hospital in Rajasthan, India: a retrospective analysis

OBJECTIVE

This study aimed to investigate the burden of the COVID-19 pandemic on tuberculosis (TB) trends, patient demographics, disease types and hospitalisation duration within the Respiratory Medicine Department over three distinct phases: pre-COVID-19, COVID-19 and post-COVID-19.

DESIGN

Retrospective analysis using electronic medical records of patients with TB admitted between June 2018 and June 2023 was done to explore the impact of COVID-19 on patients with TB. The study employed a meticulous segmentation into pre-COVID-19, COVID-19 and post-COVID-19 eras.

SETTING

National Institute of Medical Science Hospital in Jaipur, Rajasthan, India.

PRIMARY AND SECONDARY OUTCOME MEASURES

Primary outcome includes patients admitted to the Respiratory Medicine Department of the hospital and secondary outcome involves the duration of hospital stay.

RESULTS

The study encompassed 1845 subjects across the three eras, revealing a reduction in TB incidence during the post-COVID-19 era compared with the pre-COVID-19 period (p<0.01). Substantial demographic shifts were observed, with 5.2% decline in TB incidence among males in the post-COVID-19 era (n=529) compared with the pre-COVID-19 era (n=606). Despite the decrease, overall TB incidence remained significantly higher in males (n=1460) than females (n=385), with consistently elevated rates in rural (65.8%) as compared with the urban areas (34.2%). Extended hospital stays were noted in the post-COVID-19 era compared with the pre-COVID-19 era (p<0.01).

CONCLUSION

The study underscores the influence of the COVID-19 pandemic on the TB landscape and hospitalisation dynamics. Notably, patient burden of TB declined during the COVID-19 era, with a decline in the post-COVID-19 era compared with the pre-COVID-19 era. Prolonged hospitalisation in the post-COVID-19 period indicates the need for adaptive healthcare strategies and the formulation of public health policies in a post-pandemic context. These findings contribute to a comprehensive understanding of the evolving TB scenario, emphasising the necessity for tailored healthcare approaches in the aftermath of a global health crisis.

The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies

This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model's equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease's dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

Mathematical modeling and analysis of COVID-19 and TB co-dynamics

This study proposes a mathematical model for examining the COVID-19 and tuberculosis (TB) co-dynamics thoroughly. First, the single infection dynamics: COVID-19 infection and TB infection models are taken into consideration and examined. Following that, the co-dynamics with TB and COVID-19 is also investigated. In order to comprehend the developed model dynamics, the basic system attributes including the region of definition, theory of nonnegativity and boundedness of solution are investigated. Further, a qualitative analysis of the equilibria of the formulated model equations is performed. The equilibria of both infection models are globally asymptotically stable if their respective basic reproductive number is smaller than one. As the associated reproductive number reaches unity, they experience the forward bifurcation phenomenon. Additionally, it is demonstrated that the formulated co-dynamics model would not experience backward bifurcation by applying the center manifold theory. Moreover, model fitting is done by using daily reported COVID-19 cumulative data in Ethiopia between March 13, 2020, and May 31, 2022. For instance, the non-linear least squares approach of fitting a function to data was performed in the fitting process using s c i p y . o p t i m i z e . c u r v e _ f i t from the Python. Finally, to corroborate the analytical findings of the model equation, numerical simulations were conducted.

Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

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

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R₀ < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R₀ < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

A mathematical model for the co-dynamics of COVID-19 and tuberculosis

In this study, we formulated and analyzed a deterministic mathematical model for the co-infection of COVID-19 and tuberculosis, to study the co-dynamics and impact of each disease in a given population. Using each disease's corresponding reproduction number, the existence and stability of the disease-free equilibrium were established. When the respective threshold quantitiesR C , andR T are below unity, the COVID-19 and TB-free equilibrium are said to be locally asymptotically stable. The impact of vaccine (i.e., efficacy and vaccinated proportion) and the condition required for COVID-19 eradication was examined. Furthermore, the presence of the endemic equilibria of the sub-models is analyzed and the criteria for the phenomenon of backward bifurcation of the COVID-19 sub-model are presented. To better understand how each disease condition impacts the dynamics behavior of the other, we investigate the invasion criterion of each disease by computing the threshold quantity known as the invasion reproduction number. We perform a numerical simulation to investigate the impact of threshold quantities ( R C , R T ) with respect to their invasion reproduction number, co-infection transmission rate ( β c t ) , and each disease transmission rate ( β c , β t ) on disease dynamics. The outcomes established the necessity for the coexistence or elimination of both diseases from the communities. Overall, our findings imply that while COVID-19 incidence decreases with co-infection prevalence, the burden of tuberculosis on the human population increases.

Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination

COVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ω is suspended ( Ω = 0 ) is globally asymptotically stable when the effective reproduction numberR 0 c < 1 and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment ( Ω > 0 ), the endemic equilibrium using the centre manifold theory is shown to be stable globally wheneverR 0 c > 1 . The model is extended into optimal control system and analyzed analytically using Pontryagin's Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.

Comments on "Optimal control analysis of a COVID-19 and tuberculosis co-dynamics model"

Study of dynamics of COVID-19 and its co-infection with other diseases through mathematical models is the major focus of recent advancement in mathematical modeling of infectious diseases. There are numerous mathematical models on COVID-19 which describe its dynamics for different geographic regions. However, there are very few research papers dealing with co-infection of COVID-19 and TB. As both TB and COVID-19 are infectious diseases of same nature it becomes very difficult to predict the co-dynamics of these two diseases. The formulation of a correct mathematical model is very important in any kind of modeling and if the mathematical model is not proper then any prediction based on this may not be valid. This letter highlights the important limitations in the proposed mathematical model of co-dynamics of COVID-19 and TB by [1].

The COVID-19 and TB syndemic: the way forward

Together, SARS-CoV-2 and M. tuberculosis have killed approximately 5.7 million people worldwide over the past 2 years. The COVID-19 pandemic, and the non-pharmaceutical interventions to mitigate COVID-19 transmission (including social distancing regulations, partial lockdowns and quarantines), have disrupted healthcare services and led to a reallocation of resources to COVID-19 care. There has also been a tragic loss of healthcare workers who succumbed to the disease. This has had consequences for TB services, and the fear of contracting COVID-19 may also have contributed to reduced access to TB services. Altogether, this is projected to have resulted in a 5-year setback in terms of mortality from TB and a 9-year setback in terms of TB detection. In addition, past and present TB disease has been reported to increase both COVID-19 fatality and incidence. Similarly, COVID-19 may adversely affect TB outcomes. From a more positive perspective, the pandemic has also created opportunities to improve TB care. In this review, we highlight similarities and differences between these two infectious diseases, describe gaps in our knowledge and discuss solutions and priorities for future research.

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

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.

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

In co-infection models for two diseases, it is mostly claimed that, the dynamical behavior of the sub-models usually predict or drive the behavior of the complete models. However, under a certain assumption such as, allowing incident co-infection with both diseases, we have a different observation. In this paper, a new mathematical model for SARS-CoV-2 and Zika co-dynamics is presented which incorporates incident co-infection by susceptible individuals. It is worth mentioning that the assumption is missing in many existing co-infection models. We shall discuss the impact of this assumption on the dynamics of a co-infection model. The model also captures sexual transmission of Zika virus. The positivity and boundedness of solution of the proposed model are studied, in addition to the local asymptotic stability analysis. The model is shown to exhibit backward bifurcation caused by the disease-induced death rates and parameters associated with susceptibility to a second infection by those singly infected. Using Lyapunov functions, the disease free and endemic equilibria are shown to be globally asymptotically stable for R 0 1 , respectively. To manage the co-circulation of both infections effectively, under an endemic setting, time dependent controls in the form of SARS-CoV-2, Zika and co-infection prevention strategies are incorporated into the model. The simulations show that SARS-CoV-2 prevention could greatly reduce the burden of co-infections with Zika. Furthermore, it is also shown that prevention controls for Zika can significantly decrease the burden of co-infections with SARS-CoV-2.

HIV and COVID-19 co-infection: A mathematical model and optimal control

A new mathematical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models; therefore, basic analysis of the two sub-models; HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models' disease-free and endemic equilibria. Using the fmincon function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control.

Molecular and Cellular Mechanisms of M. tuberculosis and SARS-CoV-2 Infections—Unexpected Similarities of Pathogenesis and What to Expect from Co-Infection

Tuberculosis is still an important medical and social problem. In recent years, great strides have been made in the fight against M. tuberculosis, especially in the Russian Federation. However, the emergence of a new coronavirus infection (COVID-19) has led to the long-term isolation of the population on the one hand and to the relevance of using personal protective equipment on the other. Our knowledge regarding SARS-CoV-2-induced inflammation and tissue destruction is rapidly expanding, while our understanding of the pathology of human pulmonary tuberculosis gained through more the 100 years of research is still limited. This paper reviews the main molecular and cellular differences and similarities caused by M. tuberculosis and SARS-CoV-2 infections, as well as their critical immunological and pathomorphological features. Immune suppression caused by the SARS-CoV-2 virus may result in certain difficulties in the diagnosis and treatment of tuberculosis. Furthermore, long-term lymphopenia, hyperinflammation, lung tissue injury and imbalance in CD4+ T cell subsets associated with COVID-19 could propagate M. tuberculosis infection and disease progression.