Co-infection dynamics of COVID-19 and HIV/AIDS.

Although there are many results that can be used to treat and prevent Coronavirus Disease 2019 (COVID-19) and Human Immunodeficiency Virus (HIV), these diseases continue to be public health concerns and cause socioeconomic consequences. Following compromised immunity, COVID-19 is considered to be a challenge for people with HIV. People with advanced HIV are considered a vulnerable population at high risk in several case studies that discuss COVID-19 and HIV co-infection. As there is no cure for HIV and there is a chance of contracting COVID-19 again, co-infection continues to pose a problem. The purpose of this study is to investigate the impact of intervention strategies and identify the role of different parameters in risking people living with HIV to death when they get infected with COVID-19. This is achieved through the development and rigorous analysis of a mathematical model that considers a population at risk of death due to COVID-19 and HIV. The model formulation provides a detailed explanation of the transmission dynamics of COVID-19 and HIV co-infection. The solution's invariant region, positivity, and boundedness were established. The reproduction numbers of the sub-models and the co-infection model were determined. The existence and stability of equilibria, including backward bifurcation for the COVID-19 sub-model, were examined. The epidemiological significance of backward bifurcation is that the condition [Formula: see text] less than 1 for eliminating COVID-19, though necessary, is no longer sufficient. Parametric estimation and curve fitting were performed based on data from Ethiopia. Numerical simulations were employed to support and clarify the analytical findings and to show some parameter effects on COVID-19 and HIV co-infection. Accordingly, the simulations indicated that parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], related to HIV patients' exposure to other diseases and the increase in infectiousness, have a positive role in increasing the number of co-infections. On the other hand, an increase in COVID-19 vaccination ([Formula: see text]) shows the suppression of co-infection cases. In addition, treating co-infected individuals for COVID-19, increasing treatment rates [Formula: see text] and [Formula: see text], reduces the death risk of HIV-infected individuals due to the co-infection burden. It was implied that improving vaccine delivery programs and other medical interventions have important contributions to lowering the risk of COVID-19 infection-related fatalities in HIV patients.

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 scipy.optimize.curve_fit from the Python. Finally, to corroborate the analytical findings of the model equation, numerical simulations were conducted.

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 > Î·∗). 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.

Mathematical modeling and analysis for the co-infection of COVID-19 and tuberculosis.

We developed a TB-COVID-19 co-infection epidemic model using a non-linear dynamical system by subdividing the human population into seven compartments. The biological well-posedness of the formulated mathematical model was studied via proving properties like boundedness of solutions, no-negativity, and the solution's dependence on the initial data. We then computed the reproduction numbers separately for TB and COVID-19 sub-models. The criterion for stability conditions for stationary points was examined. The basic reproduction number of sub-models used to suggest the mitigation and persistence of the diseases. Qualitative analysis of the sub-models revealed that the disease-free stationary points are both locally and globally stable provided the respective reproduction numbers are smaller than unit. The endemic stationary points for each sub-models were globally stable if their respective basic reproduction numbers are greater than unit. In each sub-model, we performed an analysis of sensitive parameters concerning the corresponding reproduction numbers. Results from sensitivity indices of the parameters revealed that deceasing contact rate and increasing the transferring rates from the latent stage to an infected class of individuals leads to mitigating the two diseases and their co-infections. We have also studied the analytical behavior of the full co-infection model by deriving the equilibrium points and investigating the conditions of their stability. The numerical experiments of the proposed co-infection model agree with the findings in the analytical results.

Mathematical modelling and analysis of coffee berry disease dynamics on a coffee farm.

This paper focuses on a mathematical model for coffee berry disease infestation dynamics. This model considers coffee berry and vector populations with the interaction of fungal pathogens. In order to gain an insight into the global dynamics of coffee berry disease transmission and eradication on any given coffee farm, the assumption of logistic growth with a carrying capacity reflects the fact that the amount of coffee plants depends on the limited size of the coffee farm. First, we show that all solutions of the chosen model are bounded and non-negative with positive initial data in a feasible region. Subsequently, endemic and disease-free equilibrium points are calculated. The basic reproduction number with respect to the coffee berry disease-free equilibrium point is derived using a next generation matrix approach. Furthermore, the local stability of the equilibria is established based on the Jacobian matrix and Routh Hurwitz criteria. The global stability of the equilibria is also proved by using the Lyapunov function. Moreover, bifurcation analysis is proved by the center manifold theory. The sensitivity indices for the basic reproduction number with respect to the main parameters are determined. Finally, the numerical simulations show the agreement with the analytical results of the model analysis.

Mathematical modeling for COVID-19 transmission dynamics: A case study in Ethiopia.

In this paper, we proposed a nonlinear deterministic mathematical model for the transmission dynamics of COVID-19. First, we analyzed the system properties such as boundedness of the solutions, existence of disease-free and endemic equilibria, local and global stability of equilibrium points. Besides, we computed the basic reproduction number R 0 and studied its normalized sensitivity for model parameters to identify the most influencing parameter. The local stability of the disease-free equilibrium point is also verified via the help of the Jacobian matrix and Routh Hurwitz criteria. Moreover, the global stability of the disease-free equilibrium point is proved by using the approach of Castillo-Chavez and Song. We also proved the existence of the forward bifurcation using the center manifold theory. Then the model is fitted with COVID-19 infected cases reported from March 13, 2020, to July 31, 2021, in Ethiopia. The values of model parameters are then estimated from the data reported using the least square method together with the fminsearch function in the MATLAB optimization toolbox. Finally, different simulation cases were performed using PYTHON software to compare with analytical results. The simulation results suggest that the spread of COVID-19 can be managed via minimizing the contact rate of infected and increasing the quarantine of exposed individuals.

Farming awareness based optimum interventions for crop pest control.

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.