A Systematic Literature Review of Mathematical Models for Coinfections: Tuberculosis, Malaria, and HIV/AIDS.

Tuberculosis, malaria, and HIV are among the most lethal diseases, with AIDS (Acquired Immune Deficiency Syndrome) being a chronic and potentially life-threatening condition caused by the human immunodeficiency virus (HIV). Individually, each of these infections presents a significant health challenge. However, when tuberculosis, malaria, and HIV co-occur, the symptoms can worsen, leading to an increased mortality risk. Mathematical models have been created to study coinfections involving tuberculosis, malaria, and HIV. This systematic literature review explores the importance of coinfection models by examining articles from reputable databases such as Dimensions, ScienceDirect, Scopus, and PubMed. The primary emphasis is on investigating coinfection models related to tuberculosis, malaria, and HIV. The findings demonstrate that each article thoroughly covers various aspects, including model development, mathematical analysis, sensitivity analysis, optimal control strategies, and research discoveries. Based on our comprehensive evaluation, we offer valuable recommendations for future research efforts in this field.

A mathematical model for the transmission of co-infection with COVID-19 and kidney disease.

The world suffers from the acute respiratory syndrome COVID-19 pandemic, which will be scary if other co-existing illnesses exacerbate it. The co-occurrence of the COVID-19 virus with kidney disease has not been available in the literature. So, further research needs to be conducted to reveal the transmission dynamics of COVID-19 and kidney disease. This study aims to create mathematical models to understand how COVID-19 interacts with kidney diseases in specific populations. Therefore, the initial step was to formulate a deterministic Susceptible-Infected-Recovered (SIR) mathematical model to depict the co-infection dynamics of COVID-19 and kidney disease. A mathematical model with seven compartments has been developed using nonlinear ordinary differential equations. This model incorporates the invariant region, disease-free and endemic equilibrium, along with the positivity solution. The basic reproduction number, calculated via the next-generation matrix, allows us to assess the stability of the equilibrium. Sensitivity analysis is also utilised to understand the influence of each parameter on disease spread or containment. The results show that a surge in COVID-19 infection rates and the existence of kidney disease significantly enhances the co-infection risks. Numerical simulations further clarify the potential outcomes of treating COVID-19 alone, kidney disease alone, and co-infected cases. The study of the potential model can be utilised to maximise the benefits of simulation to minimise the global health complexity of COVID-19 and kidney disease.

Dynamic analysis and control of a rice-pest system under transcritical bifurcations.

A decision model is developed by adopting two control techniques, combining cultural methods and pesticides in a hybrid approach. To control the adverse effects in the long term and to be able to evaluate the extensive use of pesticides on the environment and nearby ecosystems, the novel decision model assumes the use of pesticides only in an emergency situation. We, therefore, formulate a rice-pest-control model by rigorously modelling a rice-pest system and including the decision model and control techniques. The model is then extended to become an optimal control system with an objective function that minimizes the annual losses of rice by controlling insect pest infestations and simultaneously reduce the adverse impacts of pesticides on the environment and nearby ecosystems. This rice-pest-control model is verified by analysis, obtains the necessary conditions for optimality, and confirms our main results numerically. The rice-pest system is verified by stability analysis at equilibrium points and shows transcritical bifurcations indicative of acceptable thresholds for insect pests to demonstrate the pest control strategy.

Modeling and optimal control applied to reduce the effects of greenhouse gases emitted from the coal-based power plant in Bangladesh.

The coal-fired power station is believed to be one of the major emitters of air pollutants, particularly carbon dioxide (CO2), which is the main sensitive driver of climate change due to global warming, consequently causing significant intimidation for the Sundarbans, the world's largest mangrove forest and nearby due to high emissions of air pollutants such as Carbon-Di-Oxide (CO2). Here, we used a compartmental mathematical model with 3 compartments to study the dynamics of greenhouse gas emissions, concentration, and uptake, which we can control by installing a chemical reactor system near the power plant and naturally afforesting the regions. The model was built from scratch to study these types of problems. First, we formulated the optimal control problem by connecting two control measurement systems: a chemical reactor system and natural afforestation. For this purpose, Pontryagin's maximum principle is used. The novelty of this work is the investigation of optimal strategies to minimize the impact of gases emitted by Coal based power plants on neighboring regions. More realistic facts such as system damage from excess emissions, most absorbers, and other facts are covered here. The numerical solution obtained illustrates the outcome of the system with initial values and theoretical parameters that best represent reality. By evaluating the performance index scores, and objective function values, we found that both controls (the chemical reactor system and natural afforestation) help minimize air pollution. We then simulated our model with 5 different control strategies to observe its performance in reducing pollutants. Once we determine that two control strategies are equally effective in reducing pollution, let's compare them by looking at the costs associated with each strategy. Therefore, using both control systems (chemical reactor and natural afforestation) with a higher reaction rate, we suggested chemical reactor system control as the best strategy.

An SEQAIHR model to study COVID-19 transmission and optimal control strategies in Hong Kong, 2022.

During the COVID-19 pandemic, one of the major concerns was a medical emergency in human society. Therefore it was necessary to control or restrict the disease spreading among populations in any fruitful way at that time. To frame out a proper policy for controlling COVID-19 spreading with limited medical facilities, here we propose an SEQAIHR model having saturated treatment. We check biological feasibility of model solutions and compute the basic reproduction number ( R 0 ). Moreover, the model exhibits transcritical, backward bifurcation and forward bifurcation with hysteresis with respect to different parameters under some restrictions. Further to validate the model, we fit it with real COVID-19 infected data of Hong Kong from 19th December, 2021 to 3rd April, 2022 and estimate model parameters. Applying sensitivity analysis, we find out the most sensitive parameters that have an effect on R 0 . We estimate R 0 using actual initial growth data of COVID-19 and calculate effective reproduction number for same period. Finally, an optimal control problem has been proposed considering effective vaccination and saturated treatment for hospitalized class to decrease density of the infected class and to minimize implemented cost.

Modeling the optimal mitigation of potential impact of climate change on coastal ecosystems.

Global warming is adversely affecting the earth's climate system due to rapid emissions of greenhouse gases (GHGs). Consequently, the world's coastal ecosystems are rapidly approaching a dangerous situation. In this study, we formulate a mathematical model to assess the impact of rapid emissions of GHGs on climate change and coastal ecosystems. Furthermore, we develop a mitigation method involving two control strategies: coastal greenbelt and desulfurization. Here, greenbelt is considered in coastal areas to reduce the concentrations of GHGs by absorbing the environmental carbon dioxide (CO2), whereas desulfurization is considered in factories and industries to reduce GHG emissions by controlling the release of harmful sulfur compounds. The model and how it can control the situation are analytically verified. Numerical results of this study are confirmed by comparison with other studies that examine different scenarios. Results show that both control strategies can mitigate GHG concentrations, curtail global warming and to some extent manage climate change. The results further reveal that both control strategies are more effective than one control method. Overall, the results suggest that the concentrations of GHGs and the effects of climate change can be controlled by adopting sufficient coastal greenbelt and desulfurization techniques in various industries.

Optimal control strategies for preventing hepatitis B infection and reducing chronic liver cirrhosis incidence.

Advanced liver cirrhosis has become life-threatening among non-communicable diseases nowadays. Cirrhosis, the terminal stage of liver diseases in which the liver develops scarring as a result of various long-term continuous damages. Among liver diseases, viral hepatitis is the major risk factor for chronic cirrhosis development. The present paper demonstrates a compartmental model of chronic disease liver cirrhosis describing the transmission dynamics of this disease. Applying the Pontryagin's maximum principle, the optimal control policies such as vaccination for hepatitis B virus and treatment of other causes of cirrhosis are adopted as control measures. The target of this study is to minimize the number of infected and liver cirrhotic individuals as well as the associated cost of the control. For this purpose, the optimal control strategies are employed according to the underlying causes behind this disease. Our goal is to find the strategy of preventing hepatitis B infection which is considered one of the leading causes of cirrhosis and consequently, reduction of the chronic cirrhosis incidence. Efficiency analysis is also performed to observe the effective control among the two control strategies. The model is investigated both analytically and numerically and the numerical simulations are carried out to illustrate the analytical findings. The analysis reveals that both the vaccination and treatment could be the most fruitful way to reduce the incidence of chronic liver cirrhosis.