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.

An Optimal Control Model to Understand the Potential Impact of the New Vaccine and Transmission-Blocking Drugs for Malaria: A Case Study in Papua and West Papua, Indonesia.

Malaria is one of the major causes of a high death rate due to infectious diseases every year. Despite attempts to eradicate the disease, results have not been very successful. New vaccines and other treatments are being constantly developed to seek optimal ways to prevent malaria outbreaks. In this article, we formulate and analyze an optimal control model of malaria incorporating the new pre-erythrocytic vaccine and transmission-blocking treatment. Sufficient conditions to guarantee local stability of the malaria-free equilibrium were derived based on the controlled reproduction number condition. Using the non-linear least square fitting method, we fitted the incidence data from the province of Papua and West Papua in Indonesia to estimate the model parameter values. The optimal control characterization and optimality conditions were derived by applying the Pontryagin Maximum Principle, and numerical simulations were also presented. Simulation results show that both the pre-erythrocytic vaccine and transmission-blocking treatment significantly reduce the spread of malaria. Accordingly, a high doses of pre-erythrocytic vaccine is needed if the number of infected individuals is relatively small, while transmission blocking is required if the number of infected individuals is relatively large. These results suggest that a large-scale implementation of both strategies is vital as the world continues with the effort to eradicate malaria, especially in endemic regions across the globe.

Optimal control problem arising from COVID-19 transmission model with rapid-test.

The world health organization (WHO) has declared the Coronavirus (COVID-19) a pandemic. In light of this ongoing global issue, different health and safety measure has been recommended by the WHO to ensure the proactive, comprehensive, and coordinated steps to bring back the whole world into a normal situation. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates which consider the rapid-test as the intervention program. Therefore, we have developed the biologically feasible region, i.e., positively invariant for the model and boundedness solution of the system. Our system becomes well-posed mathematically and epidemiologically for sensitive analysis and our analytical result shows an occurrence of a forward bifurcation when the basic reproduction number is equal to unity. Further, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half-normalizations, and full normalizations. The numerical approximations have been measured by using System Biology Toolbox (SBedit) with MATLAB, and the model is analyzed graphically. Our result on the sensitivity analysis shows a potential of rapid-test for the eradication program of COVID-19. Therefore, we continue our result by reconstructing our model as an optimal control problem. Our numerical simulation shows a time-dependent rapid test intervention succeeded in suppressing the spread of COVID-19 effectively with a low cost of the intervention. Finally, we forecast three COVID-19 incidence data from China, Italy, and Pakistan. Our result suggests that Italy already shows a decreasing trend of cases, while Pakistan is getting closer to the peak of COVID-19.

A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: The case of Jakarta, Indonesia.

The aim of this study is to investigate the effects of rapid testing and social distancing in controlling the spread of COVID-19, particularly in the city of Jakarta, Indonesia. We formulate a modified susceptible exposed infectious recovered compartmental model considering asymptomatic individuals. Rapid testing is intended to trace the existence of asymptomatic infected individuals among the population. This asymptomatic class is categorized into two subclasses: detected and undetected asymptomatic individuals. Furthermore, the model considers the limitations of medical resources to treat an infected individual in a hospital. The model shows two types of equilibrium point: COVID-19 free and COVID-19 endemic. The COVID-19-free equilibrium point is locally and asymptotically stable if the basic reproduction number ( R 0 ) is less than unity. In contrast, COVID-19-endemic equilibrium always exists when R 0 > 1 . The model can also show a backward bifurcation at R 0 = 1 whenever the treatment saturation parameter, which describes the hospital capacity, is larger than a specific threshold. To justify the model parameters, we use the incidence data from the city of Jakarta, Indonesia. The data pertain to infected individuals who self-isolate in their homes and visit the hospital for further treatment. Our numerical experiments indicate that strict social distancing has the potential to succeed in reducing and delaying the time of an outbreak. However, if the strict social distancing policy is relaxed, a massive rapid-test intervention should be conducted to avoid a large-scale outbreak in the future.

A quantitative and qualitative analysis of the COVID-19 pandemic model.

Global efforts around the world are focused on to discuss several health care strategies for minimizing the impact of the new coronavirus (COVID-19) on the community. As it is clear that this virus becomes a public health threat and spreading easily among individuals. Mathematical models with computational simulations are effective tools that help global efforts to estimate key transmission parameters and further improvements for controlling this disease. This is an infectious disease and can be modeled as a system of non-linear differential equations with reaction rates. This work reviews and develops some suggested models for the COVID-19 that can address important questions about global health care and suggest important notes. Then, we suggest an updated model that includes a system of differential equations with transmission parameters. Some key computational simulations and sensitivity analysis are investigated. Also, the local sensitivities for each model state concerning the model parameters are computed using three different techniques: non-normalizations, half normalizations, and full normalizations. Results based on the computational simulations show that the model dynamics are significantly changed for different key model parameters. Interestingly, we identify that transition rates between asymptomatic infected with both reported and unreported symptomatic infected individuals are very sensitive parameters concerning model variables in spreading this disease. This helps international efforts to reduce the number of infected individuals from the disease and to prevent the propagation of new coronavirus more widely on the community. Another novelty of this paper is the identification of the critical model parameters, which makes it easy to be used by biologists with less knowledge of mathematical modeling and also facilitates the improvement of the model for future development theoretically and practically.