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

Optimal control strategies on HIV/AIDS and pneumonia co-infection with mathematical modelling approach

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore, we have investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community.

Robustness and exploration between the interplay of the nonlinear co-dynamics HIV/AIDS and pneumonia model via fractional differential operators and a probabilistic approach

In this article, we considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia (H/A-P) co-infection in a human population at different infection stages. Understanding the complexities of co-dynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of H/A-P in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Furthermore, adequate prerequisites are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system's long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical techniques, power law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of H/A-P minimizes the propagation of the co-dynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in H/A-P co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and condom use, and finally, case detection as a standalone strategy.

Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics

Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals' co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin's Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.

Vaccination impact on impending HIV-COVID-19 dual epidemic with autogenous behavior modification: Hill-type functional response and premeditated optimization technique

An HIV-COVID-19 co-infection dynamics is modeled mathematically assimilating the vaccination mechanism that incorporates endogenous modification of human practices generated by the COVID-19 prevalence, absorbing the relevance of the treatment mechanism in suppressing the co-infection burden. Envisaging a COVID-19 situation, the HIV-subsystem is analyzed by introducing COVID-19 vaccination for the HIV-infected population as a prevention, and the "vaccination influenced basic reproduction number" of HIV is derived. The mono-infection systems experience forward bifurcation that evidences the persistence of diseases above unit epidemic thresholds. Delicate simulation methodologies are employed to explore the impacts of baseline vaccination, prevalence-dependent spontaneous behavioral change that induces supplementary vaccination, and medication on the dual epidemic. Captivatingly, a paradox is revealed showing that people start to get vaccinated at an additional rate with the increased COVID-19 prevalence, which ultimately diminishes the dual epidemic load. It suggests increasing the baseline vaccination rate and the potency of propagated awareness. Co-infection treatment needs to be emphasized parallelly with single infection medication under dual epidemic situations. Further, an optimization technique is introduced to the co-infection model integrating vaccination and treatment control mechanisms, which approves the strategy combining vaccination with awareness and medication as the ideal one for epidemic and economic gain. Conclusively, it is manifested that waiting frivolously for any anticipated outbreak, depending on autogenous behavior modification generated by the increased COVID-19 prevalence, instead of elevating vaccination campaigns and the efficacy of awareness beforehand, may cause devastation to the population under future co-epidemic conditions.

Computational study of a co-infection model of HIV/AIDS and hepatitis C virus models

Hepatitis C infection and HIV/AIDS contaminations are normal in certain areas of the world, and because of their geographic overlap, co-infection can't be precluded as the two illnesses have a similar transmission course. This current work presents a co-infection model of HIV/AIDS and Hepatitis C virus with fuzzy parameters. The application of fuzzy theory aids in tackling the issues associated with measuring uncertainty in the mathematical depiction of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been determined in this context, focusing on a model applicable to a specific group defined by a triangular membership function. Furthermore, for the model, a fuzzy non-standard finite difference (NSFD) technique has been developed, and its convergence is examined within a fuzzy framework. The suggested model is numerically validated, confirming the dependability of the devised NSFD technique, which successfully retains all of the key properties of a continuous dynamical system.

A dynamical analysis and numerical simulation of COVID-19 and HIV/AIDS co-infection with intervention strategies

HIV/AIDS-COVID-19 co-infection is a major public health concern especially in developing countries of the world. This paper presents HIV/AIDS-COVID-19 co-infection to investigate the impact of interventions on its transmission using ordinary differential equation. In the analysis of the model, the solutions are shown to be non-negative and bounded, using next-generation matrix approach the basic reproduction numbers are computed, sufficient conditions for stabilities of equilibrium points are established. The sensitivity analysis showed that transmission rates are the most sensitive parameters that have direct impact on the basic reproduction numbers and protection and treatment rates are more sensitive and have indirect impact to the basic reproduction numbers. Numerical simulations shown that some parameter effects on the transmission of single infections as well as co-infection, and applying the protection rates and treatment rates have effective roles to minimize and also to eradicate the HIV/AIDS-COVID-19 co-infection spreading in the community.

Investigating the Effects of Intervention Strategies on Pneumonia and HIV/AIDS Coinfection Model

HIV/AIDS and pneumonia coinfection have imposed a major socioeconomic and health burden throughout the world, especially in the developing countries. In this study, we propose a compartmental epidemic model on the spreading dynamics of HIV/AIDS and pneumonia coinfection to investigate the impacts of protection and treatment intervention mechanisms on the coinfection spreading in the community. In the qualitative analysis of the model, we have performed the positivity and boundedness of the coinfection model solutions; the effective reproduction numbers using the next-generation operator approach; and both the disease-free and endemic equilibrium points' local and global stabilities using the Routh-Hurwiz and Castillo-Chavez stability criteria, respectively. We performed the sensitivity analysis of the model parameters using both the forward normalized sensitivity index criteria and numerical methods (simulation). Moreover, we carried out the numerical simulation for different scenarios to investigate the effect of model parameters on the associated reproduction number, the effect of model parameters on the model state variables, and the solution behavior and convergence to the equilibrium point(s) of the models. Finally, from the qualitative analysis and numerical simulation results, we observed that the disease-spreading rates, protection rates, and treatment rates are the most sensitive parameters, and we recommend for stakeholders to concentrate and exert their maximum effort to minimize the spreading rates by maximizing the protection and treatment rates.

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.

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.

Analysis of HBV and COVID-19 Coinfection Model with Intervention Strategies

Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

Modelling the dynamics of acute and chronic hepatitis B with optimal control

This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin's Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control

Clinical reports have shown that chronic hepatitis B virus (HBV) patients co-infected with SARS-CoV-2 have a higher risk of complications with liver disease than patients without SARS-CoV-2. In this work, a co-dynamical model is designed for SARS-CoV-2 and HBV which incorporates incident infection with the dual diseases. Existence of boundary and co-existence endemic equilibria are proved. The occurrence of backward bifurcation, in the absence and presence of incident co-infection, is investigated through the proposed model. It is noted that in the absence of incident co-infection, backward bifurcation is not observed in the model. However, incident co-infection triggers this phenomenon. For a special case of the study, the disease free and endemic equilibria are shown to be globally asymptotically stable. To contain the spread of both infections in case of an endemic situation, the time dependent controls are incorporated in the model. Also, global sensitivity analysis is carried out by using appropriate ranges of the parameter values which helps to assess their level of sensitivity with reference to the reproduction numbers and the infected components of the model. Finally, numerical assessment of the control system using various intervention strategies is performed, and reached at the conclusion that enhanced preventive efforts against incident co-infection could remarkably control the co-circulation of both SARS-CoV-2 and HBV.

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.