Optimal control of pneumonia transmission model with seasonal factor: Learning from Jakarta incidence data

A dynamical model of drinking and smoking with optimal control analysis

The intake of alcohol is dangerous, and the smoking of tobacco is savage, but it is life-threatening to practice both smoking and drinking. According to the World Health Organisation, the world loses about 8.5 million people each year as a result of smoking tobacco and drinking alcohol. To study this, we present a mathematical model that investigates the co-dynamics of alcohol drinking and tobacco smoking, as well as some control strategies. In contrast, many studies focus solely on the dynamics of alcohol consumption or tobacco smoking. Also, these studies assume that an individual who may recover from both alcohol drinking and tobacco smoking may relapse. We determined the basic reproductive number by employing the next-generation matrix approach. We conducted local and global stability analyses for the drinking, smoking-free, and endemic states. We then conducted extensive research into secondary infections related to smoking and drinking. We then performed numerical simulations and analysis using the parameter values from the literature. The study further examined the influence of some key parameters on secondary co-dependence infections, which occur when one infected individual enters the population and recovers from both over time. For example, in this study, it was shown that the contact rates a1 and a2 have a direct relationship to the spread of drinking and smoking. In contrast, recovery rates δ1, δ2 showed an inverse relationship. In addition, we conducted an optimal control analysis by suggesting the following: drinking prevention efforts, smoking prevention efforts, recovery efforts on the co-dependence of drinking and smoking, recovery efforts on drinking, and recovery efforts on smoking. The simulations indicated that using these controls can help reduce the number of smokers and drinkers within eight weeks.

Improving tuberculosis control: assessing the value of medical masks and case detection-a multi-country study with cost-effectiveness analysis

Tuberculosis (TB) remains a significant global health concern, necessitating effective control strategies. This article presents a mathematical model to evaluate the comparative effectiveness of medical mask usage and case detection in TB control. The model is constructed as a system of ordinary differential equations and incorporates crucial aspects of TB dynamics, including slow-fast progression, medical mask use, case detection, treatment interventions and differentiation between symptomatic and asymptomatic cases. A key objective of TB control is to ensure that the reproduction number,R c , remains below unity to achieve TB elimination or persistence ifR c exceeds 1. Our mathematical analysis reveals the presence of a transcritical bifurcation when theR c = 1 signifies a critical juncture in TB control strategies. These results confirm that the effectiveness of case detection in diminishing the endemic population of symptomatic individuals within a TB-endemic equilibrium depends on exceeding a critical threshold value. Furthermore, our model is calibrated using TB yearly case incidence data per 100 000 population from Indonesia, India, Lesotho and Angola. We employed the bootstrap resampling residual approach to assess the uncertainty inherent in our parameter estimates which provides a comprehensive distribution of the parameter values. Despite a declining trend in new incidence, these four countries exhibit a reproduction number greater than 1, indicating persistent TB cases in the presence of ongoing TB control programmes. We employ the partial rank correlation coefficient in conjunction with the Latin hypercube sampling method to conduct a global sensitivity analysis of theR c parameter for each fitted parameter in every country. We find that the medical mask use is more sensitive to reduceR c compared with the case detection implementation. To further gain insight into the necessary control strategy, we formulated an optimal control and studied the cost-effectiveness analysis of our model to investigate the impact of case detection and medical mask use as control measures in TB spread. Cost-effectiveness analysis demonstrates that combining these interventions emerges as the most cost-effective strategy for TB control. Our findings highlight the critical importance of medical masks and their efficacy coupled with case detection in shaping TB control dynamics, elucidating the primary parameter of concern for managing the control reproduction number. We envisage our findings to have implications and be vital for TB control if implemented by policymakers and healthcare practitioners involved in TB control efforts.

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.

A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies

This study developed a deterministic transmission model for the coronavirus disease of 2019 (COVID-19), considering various factors such as vaccination, awareness, quarantine, and treatment resource limitations for infected individuals in quarantine facilities. The proposed model comprised five compartments: susceptible, vaccinated, quarantined, infected, and recovery. It also considered awareness and limited resources by using a saturated function. Dynamic analyses, including equilibrium points, control reproduction numbers, and bifurcation analyses, were conducted in this research, employing analytics to derive insights. Our results indicated the possibility of an endemic equilibrium even if the reproduction number for control was less than one. Using incidence data from West Java, Indonesia, we estimated our model parameter values to calibrate them with the real situation in the field. Elasticity analysis highlighted the crucial role of contact restrictions in reducing the spread of COVID-19, especially when combined with community awareness. This emphasized the analytics-driven nature of our approach. We transformed our model into an optimal control framework due to budget constraints. Leveraging Pontriagin's maximum principle, we meticulously formulated and solved our optimal control problem using the forward-backward sweep method. Our experiments underscored the pivotal role of vaccination in infection containment. Vaccination effectively reduces the risk of infection among vaccinated individuals, leading to a lower overall infection rate. However, combining vaccination and quarantine measures yields even more promising results than vaccination alone. A second crucial finding emphasized the need for early intervention during outbreaks rather than delayed responses. Early interventions significantly reduce the number of preventable infections, underscoring their importance.