A DFT investigation of lead-free TlSnX3 (X = Cl, Br, or I) perovskites for potential applications in solar cells and thermoelectric devices

In the present study, the Density Functional Theory (DFT) was employed to computationally investigate the potential application of newly developed lead-free perovskites with the formula of TlSnX3 (X = Cl, Br, or I) as absorbers in the perovskite solar cells and as thermoelectric materials. The Quantum Espresso code was implemented to optimize the structural configuration of the perovskites and to compute a range of their properties, including their elasticity, electronic behavior, optical characteristics, and thermoelectric attributes. The findings indicated that these perovskite materials exhibit both chemical and structural stability and that TlSnBr3 and TlSnI3 perovskites possess high dynamic stability. The findings additionally revealed direct (R → R) band gap energy values of 0.87 eV for TlSnCl3, 0.52 eV for TlSnBr3, and 0.28 eV for TlSnI3 using the GGA-PBE functional. Further analysis of their elastic properties suggested that these materials are mechanically stable and displayed overall ductile behaviour. They also demonstrated remarkable optical properties, particularly a high absorption coefficient, ranging from 105 cm-1 to 106 cm-1. Consequently, it is reasonable to infer that these materials exhibit considerable potential for utilization in solar cells. Finally, the evaluation of their thermoelectric properties has revealed the highly promising potential of these materials to be employed in thermoelectric applications.

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

Pneumonia is a dangerous disease that can lead to death without proper treatment. It is caused by a bacterial infection that leads to the inflammation of the air sacs in human lungs and potentially results in a lung abscess if not properly untreated. Here in this article we introduced a novel mathematical model to investigate the potential impact of Pneumonia treatments on disease transmission dynamics. The model is then validated against data from Jakarta City, Indonesia. In the model, the infection stage in infected individuals is categorized into three stages: the Exposed, Congestion and Hepatization, and the Resolution stage. Mathematical analysis shows that the disease-free equilibrium is always locally asymptotically stable when the basic reproduction number is less than one and unstable when larger than one. The endemic equilibrium only exists when the basic reproduction number is larger than one. Our proposed model always exhibits a forward bifurcation when the basic reproduction number is equal to one, which indicates local stability of the endemic equilibrium when the basic reproduction number is larger than one but close to one. A global sensitivity analysis shows that the infection parameter is the most influential parameter in determining the size of the total infected individual in the endemic equilibrium point. Furthermore, we also found that the hospitalization and the acceleration of the treatment duration can be used to control the level of endemic size. An optimal control problem was constructed from the earlier model and analyzed using the Pontryagin Maximum Principle. We find that the implementation of treatment in the earlier stage of infected individuals is needed to avoid a more significant outbreak of Pneumonia in a long-term intervention.

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

Dengue is a public health problem with around 390 million cases annually and is caused by four distinct serotypes. Infection by one of the serotypes provides lifelong immunity to that serotype but have a higher chance of attracting the more dangerous forms of dengue in subsequent infections. Therefore, a perfect strategy against dengue is required. Dengue vaccine with 42-80% efficacy level has been licensed for the use in reducing disease transmission. However, this may increase the likelihood of obtaining the dangerous forms of dengue. In this paper, we have developed single and two-serotype dengue mathematical models to investigate the effects of vaccination on dengue transmission dynamics. The model is validated against dengue data from Kupang city, Indonesia. We investigate the effects of vaccination on seronegative and seropositive individuals and perform a global sensitivity analysis to determine the most influential parameters of the model. A sensitivity analysis suggests that the vaccination rate, the transmission probability and the biting rate have greater effects on the reduction of the proportion of dengue cases. Interestingly, with vaccine implementation, the mosquito-related parameters do not have significant impact on the reduction in the proportion of dengue cases. If the vaccination is implemented on seronegative individuals only, it may increase the likelihood of obtaining the severe dengue. To reduce the proportion of severe dengue cases, it is better to vaccinate seropositive individuals. In the context of Kupang City where the majority of individuals have been infected by at least one dengue serotype, the implementation of vaccination strategy is possible. However, understanding the serotype-specific differences is required to optimise the delivery of the intervention.

Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness

A total of more than 27 million confirmed cases of the novel coronavirus outbreak, also known as COVID-19, have been reported as of September 7, 2020. To reduce its transmission, a number of strategies have been proposed. In this study, mathematical models with nonpharmaceutical and pharmaceutical interventions were formulated and analyzed. The first model was formulated without the inclusion of community awareness. The analysis focused on investigating the mathematical behavior of the model, which can explain how medical masks, medical treatment, and rapid testing can be used to suppress the spread of COVID-19. In the second model, community awareness was taken into account, and all the interventions considered were represented as time-dependent parameters. Using the center-manifold theorem, we showed that both models exhibit forward bifurcation. The infection parameters were obtained by fitting the model to COVID-19 incidence data from three provinces in Indonesia, namely, Jakarta, West Java, and East Java. Furthermore, a global sensitivity analysis was performed to identify the most influential parameters on the number of new infections and the basic reproduction number. We found that the use of medical masks has the greatest effect in determining the number of new infections. The optimal control problem from the second model was characterized using the well-known Pontryagin's maximum principle and solved numerically. The results of a cost-effectiveness analysis showed that community awareness plays a crucial role in determining the success of COVID-19 eradication programs.

Optimal control strategy for the effects of hard water consumption on kidney-related diseases

OBJECTIVES : We study the optimal control strategy for the effects of hard water consumption on kidney-related diseases. The mathematical model has been formulated and studied to gain insights on the optimal control strategy on the effects of hard-water consumption on kidney-related diseases. The positivity and boundedness of the solutions are determined. A global sensitivity analysis has been performed and the numerical solutions have been carried out. RESULTS : A global sensitivity analysis shows that the control on water is an important parameter. This can reduce the proportion of individuals with kidney-dysfunction and hence reduces the proportion of individuals with kidney-related diseases. Furthermore, the numerical solutions show that with the optimal control, the proportion of individuals with kidney-related diseases can be minimised.

Fibonacci numbers: A population dynamics perspective

Fibonacci numbers or Fibonacci sequence is among the most popular numbers or sequence in Mathematics. In this paper, we discuss the sequence in a population dynamics perspective. We discuss the early development of the sequence and interpret the sequence as a number of a hypothetical population. The governing equation that produces the Fibonacci sequence is written in a matrix form having a square matrix A. We show the relation of the eigenvalues, eigenvectors, and eigenspaces to the matrix with the dynamics of the sequence. We also generalize the matrix equation so that it governs a more realistic model of the hypothetical population. Some results regarding the modified golden ratio are presented.

The effect of Wolbachia on dengue outbreaks when dengue is repeatedly introduced

Use of the Wolbachia bacterium is a proposed new strategy to reduce dengue transmission, which results in around 390 million individuals infected annually. In places with strong variations in climatic conditions such as temperature and rainfall, dengue epidemics generally occur only at a certain time of the year. Where dengue is not endemic, the time of year in which imported cases enter the population plays a crucial role in determining the likelihood of outbreak occurrence. We use a mathematical model to study the effects of Wolbachia on dengue transmission dynamics and dengue seasonality. We focus in regions where dengue is not endemic but can spread due to the presence of a dengue vector and the arrival of people with dengue on a regular basis. Our results show that the time-window in which outbreaks can occur is reduced in the presence of Wolbachia-carrying Aedes aegypti mosquitoes by up to six weeks each year. We find that Wolbachia reduces overall case numbers by up to 80%. The strongest effect is obtained when the amplitude of the seasonal forcing is low (0.02-0.30). The benefits of Wolbachia also depend on the transmission rate, with the bacteria most effective at moderate transmission rates ranging between 0.08-0.12. Such rates are consistent with fitted estimates for Cairns, Australia.