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

Modelling measles transmission dynamics and the impact of control strategies on outbreak Management

Measles is a highly contagious and potentially fatal disease, despite the availability of effective immunizations. This study formulates a deterministic mathematical model to investigate the transmission dynamics of measles, with eight compartments representing different epidemiological states such as susceptible, vaccinated, exposed, infected, early-treated, delayed-treated, hospitalized, and recovered individuals. We use the Next Generation Matrix (NGN) approach to obtain the basic reproduction number (R 0 ) and examine local stability at the disease-free equilibrium (DFE). Sensitivity analysis with Partial Rank Correlation Coefficients (PRCC) identifies significant parameters influencing disease dynamics, such as vaccination rates, transmission rate, treatment timings, and disease-induced mortality rates. Simulation results show that delayed therapy has a limited effect on lowering the infected population, emphasizing the importance of immediate intervention. Early treatment considerably reduces the number of infected individuals, whereas improved recovery rates in hospitalized cases result in fewer hospitalizations. Vaccination is extremely successful, with increased rates significantly lowering the susceptible population while boosting the vaccinated population. Higher disease-related mortality rates reduce the afflicted population, stressing the importance of strong control methods. The transmission rate has a substantial impact on infection rates and hospitalizations, emphasizing the need for effective public health policies and healthcare capacity. The combined effect of immunization and early treatment provides useful information for optimizing control measures. This study emphasizes the need of quick and effective measures in managing measles outbreaks and serves as a platform for future research into improved public health methods.

Co-infection mathematical model for HIV/AIDS and tuberculosis with optimal control in Ethiopia

The co-epidemics of HIV/AIDS and Tuberculosis (TB) outbreak is one of a serious disease in Ethiopia that demands integrative approaches to combat its transmission. In contrast, epidemiological co-infection models often considered a single latent case and recovered individuals with TB. To bridge this gap, we presented a new optimal HIV-TB co-infection model that considers both high risk and low risk latent TB cases with taking into account preventive efforts of both HIV and TB diseases, case finding for TB and HIV/AIDS treatment. This study aimed to develop optimal HIV/AIDS-TB co-infection mathematical model to explore the best cost-effective measure to mitigate the disease burden. The model is analysed analytically by firstly segregating TB and HIV only sub models followed by the full TB-HIV co-infection model. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) points are found and the basic reproduction number R0 is obtained using the next generation matrix method (NGM). Based on the threshold value R0, the stabilities of equilibria for each sub-model are analysed. The DFE point is locally asymptotically stable when R0 < 1 and unstable when R0 > 1. The EE point is also asymptotically stable when R0 > 1 and does not exist otherwise. At R0 = 1, the existence of backward bifurcation phenomena is discussed. To curtail the cost and disease fatality, an optimal control model is formulated via time based controlling efforts. The optimal mathematical model is analysed both analytically and numerically. The numerical results are presented for two or more control measures at a time. In addition, the Incremental Cost-Effectiveness Ratio(ICER) has identified the best strategy which is crucial in limited resource. Hence, the model outcomes illustrated that applying HIV/AIDS prevention efforts and TB case finding concurrently is the most cost-effective strategy to offer substantial relief from the burden of the pandemic in the community. All results found in this study have significant public health lessons. We anticipated that the results will notify evidence based approaches to control the disease. Thus, this study will aids in the fight against HIV/AIDS, TB, and their co-infection policy-makers and other concerned organizations.

Machine learning investigation of tuberculosis with medicine immunity impact

Tuberculosis (T.B.) remains a prominent global cause of health challenges and death, exacerbated by drug-resistant strains such as multidrug-resistant tuberculosis MDR-TB and extensively drug-resistant tuberculosis XDR-TB. For an effective disease management strategy, it is crucial to understand the dynamics of T.B. infection and the impacts of treatment. In the present article, we employ AI-based machine learning techniques to investigate the immunity impact of medications. SEIPR epidemiological model is incorporated with MDR-TB for compartments susceptible to disease, exposed to risk, infected ones, preventive or resistant to initial treatment, and recovered or healed population. These masses' natural trends, effects, and interactions are formulated and described in the present study. Computations and stability analysis are conducted upon endemic and disease-free equilibria in the present model for their global scenario. Both numerical and AI-based nonlinear autoregressive exogenous NARX analyses are presented with incorporating immediate treatment and delay in treatment. This study shows that the active patients and MDR-TB, both strains, exist because of the absence of permanent immunity to T.B. Furthermore, patients who have recovered from tuberculosis may become susceptible again by losing their immunity and contributing to transmission again. This article aims to identify patterns and predictors of treatment success. The findings from this research can contribute to developing more effective tuberculosis interventions.

Optimal time-dependent SUC model for COVID-19 pandemic in India

In this paper, we propose a numerical algorithm to obtain the optimal epidemic parameters for a time-dependent Susceptible-Unidentified infected-Confirmed (tSUC) model. The tSUC model was developed to investigate the epidemiology of unconfirmed infection cases over an extended period. Among the epidemic parameters, the transmission rate can fluctuate significantly or remain stable due to various factors. For instance, if early intervention in an epidemic fails, the transmission rate may increase, whereas appropriate policies, including strict public health measures, can reduce the transmission rate. Therefore, we adaptively estimate the transmission rate to the given data using the linear change points of the number of new confirmed cases by the given cumulative confirmed data set, and the time-dependent transmission rate is interpolated based on the estimated transmission rates at linear change points. The proposed numerical algorithm preprocesses actual cumulative confirmed cases in India to smooth it and uses the preprocessed data to identify linear change points. Using these linear change points and the tSUC model, it finds the optimal time-dependent parameters that minimize the difference between the actual cumulative confirmed cases and the computed numerical solution in the least-squares sense. Numerical experiments demonstrate the numerical solution of the tSUC model using the optimal time-dependent parameters found by the proposed algorithm, validating the performance of the algorithm. Consequently, the proposed numerical algorithm calculates the time-dependent transmission rate for the actual cumulative confirmed cases in India, which can serve as a basis for analyzing the COVID-19 pandemic in India.

Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator

COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease's status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.

The role of delay in vaccination rate on Covid-19

The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.