AbstractThe HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the ...HIV-positive who do not take ART, people receiving ART treatment, people with AIDS who do not receive any treatment (full-blown AIDS), and the recovered. This model takes into account the analysis of the multiple interactions between the uneducated and the educated subpopulations, the HIV-positive who take and who do not take ART. The free-disease and endemic equilibrium points, as well as the basic reproduction number Formula: see text as a limit condition for infection-free and endemic occurrence, were produced by a mathematical analysis. The center-manifold hypothesis was used to prove that a backward bifurcation exists. The free-disease and endemic equilibrium points coexist when Formula: see text This means that HIV/AIDS is still spreading. A basic reproduction number below one is insufficient to constitute a free-disease condition. In order to determine essential parameters that significantly contribute to HIV/AIDS transmission, we computed sensitivity index values using a sensitivity analysis. The HIV/AIDS model and bifurcation parameter both identified the rate of HIV transmission from uneducated individuals to HIV-positive individuals who do not receive ART as the most crucial parameter. A numerical simulation supports the dynamical analysis.
India is one of the world's largest producers of tree nuts, yet it paradoxically remains a net importer of these commodities. This study aims to analyze the demand for imported tree nuts in India, ...motivated by the need to understand the factors contributing to this imbalance. The primary objective is to calculate income elasticities and own- and cross-price elasticities for five categories of imported tree nuts using the linear approximate almost ideal demand system model. Data is sourced from monthly import records from the United Nations Comtrade database covering 2014 to 2022. The tree nuts considered are almonds, cashews, pistachios, walnuts, and hazelnuts. Key findings reveal all imported tree nuts are normal goods. Cashews exhibit income elasticity (1.2), indicating a significant demand increase with rising incomes, while other nuts show income inelasticity. Cashews are price-elastic (−1.3), while other nuts are price-inelastic. Compensated cross-price elasticities indicate notable substitution effects, particularly between almonds and cashews. The study recommends enhancing domestic cashew production to meet growing demand and developing targeted marketing strategies to address competitive dynamics within the tree nut market. These strategies aim to reduce India's dependency on imports and promote a balanced, sustainable domestic market.
A novel HIV/AIDS infection model incorporating memory and media coverage effect is formulated. First, we introduce fractional-order derivative to the model. The basic reproduction number R0 is ...calculated using the next generation matrix method. Existence, uniqueness, and positivity of the solution of the model are investigated. Existence and local stability analysis of the equilibria of the model are discussed. The disease dies out when R0<1 at which the disease-free equilibrium is locally asymptotically stable. While the disease persists if R0>1 at which the disease-free equilibrium becomes unstable and the endemic equilibrium point emerges. Second, a time-delay, τ, is introduced to model the effect of the delayed-induced treatment. The disease-free equilibrium is locally asymptotically stable for all τ>0.
•A novel HIV/AIDS model with memory and media coverage is formulated.•First, fractional-order derivative is introduced.•Local stability analysis of equilibria is investigated.•Second, time delay is introduced.•The disease-free equilibrium is locally stable for all time delays.
•Urban and rural energy rebound effects in Beijing are studied by LA-AIDS model.•Energy rebound from substitution and income effects is decomposed by Slutsky equation.•Energy rebound effect of rural ...residents exceeded that of urban residents after 2010.•The income effect is the main source of the energy rebound effect in Beijing.•Energy rebound caused by various commodity groups presents obvious heterogeneity.
With Beijing facing greater pressure for energy conservation, improving energy efficiency becomes more necessary. However, the energy rebound effect may weaken this energy-saving effect. Using the LA-AIDS (Linear Approximation of the Almost Ideal Demand System) model and simulation analysis, this paper evaluates the energy rebound effects of different commodity groups in Beijing’s urban and rural households during 2000–2019. Then, the Slutsky decomposition equation is introduced to decompose the energy rebound caused by the substitution and income effects. Results suggest that: (1) The energy consumption of urban and rural residents shows a partial rebound in most years, and the energy rebound effect of rural residents exceeded that of urban residents after 2010. (2) The income effect from commodity price changes is the main source of the energy rebound effect both in urban and rural households. (3) The commodity groups Residence, Household facilities & Services, Transportation & Communication and Health care & Medical services have the same influencing direction on the energy rebound effect in urban and rural residents, while the commodity groups Food, Tobacco & Alcohol, Clothing and Culture, Education & Entertainment have different influencing direction. Finally, suggestions are provided for alleviating the energy rebound effect of households in Beijing.
•A stochastic staged progression AIDS model with staged treatment and second-order perturbation is studied.•The existence and uniqueness of the ergodic stationary distribution is obtained under the ...condition of.•If, we obtain that the AIDS epidemic will go to extinction in long-term.
Focusing on deterministic AIDS model proposed by Hyman (2000) and the detailed data from the World Health Organization (WHO), there are three stages of AIDS process which are described as Acute infection period, Asymptomatic phase and AIDS stage. Our paper is therefore concerned with a stochastic staged progression AIDS model with staged treatment. In view of the complexity of random disturbances, we reasonably take second-order perturbation into consideration for realistic sense. By means of our creative transformation technique and stochastic Lyapunov method, a critical value R0H>1 is firstly obtained for the existence and uniqueness of ergodic stationary distribution to the stochastic system. Not only does it respectively reveal the corresponding dynamical effects of the linear and second-order perturbations to the model, but the unified form of second-order and linear fluctuations is derived. Next, some sufficient conditions about extinction of stochastic system are established in view of the basic reproduction number R0. Finally, some examples and numerical simulations are introduced to illustrate our analytical results. In addition, some advantages of our new method and theory are highlighted by comparison with other existing results at the end of this paper.
•A higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration is studied.•We derive sufficient criteria for the existence and uniqueness of an ergodic ...stationary distribution.•The existence of a stationary distribution indicates that the infectious disease will be prevalent.•We make up adequate criteria for complete eradication and wiping out of the infectious disease.
In this paper, we study the dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration. We derive sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological point of view, the existence of a stationary distribution indicates that the infectious disease will be prevalent and persistent in the population. Moreover, we make up adequate criteria for complete eradication and wiping out of the infectious disease. Finally, we introduce some numerical simulations to confirm the theoretical results.
In this paper, by using Itô's formula, we study the dynamic behaviors of a stochastic human immune deficiency virus (HIV) model, which describes Acquired Immune Deficiency Syndrome (AIDS) with the ...effect of treatment. First, we discuss the global positivity of the solution to such a model with positive initial value. Then, we consider the limiting behavior of the solution. Moreover, we obtain the sufficient condition to guarantee the extinction of AIDS. Meanwhile, by constructing an appropriate Lyapunov function, we prove that the solution has a unique ergodic stationary distribution under a certain assumptions. Finally, we illustrate the validity of our results by numerical simulations.
Introduction: Considering the role which meat and its products play in providing the animal protein in nutrition and share a large share in the household food expenditure portfolio, and the desire to ...consume it is a significant matter in the country's consumer culture (Zhang et al, 2018), and any research and study about subject matter is important in terms of the method, purpose and scope of it at all times due to understanding present realities and through this, effective and influential elements, especially advertising, are identified from the point of view of supply and demand and by understanding it to create a balance point. Optimally, it provides well-being and proper nutrition for the community which can be an introduction to more accurate planning and more doctrinaire be considered (Korir et al, 2018). According to the studies, the demand for meat and its products in different provinces of Iran is of great importance to implement and plan policies. Therefore, this study aimed to investigate the effects of public advertising on demand for sausage and sausage meat products in Shiraz city. Material and methods: Regarding the nature of the subject and its objectives, the present study is a descriptive-analytical study, in which the information and data required in this study were collected via a cross-sectional questionnaire from 500 Shirazi citizens. To calculate the number of samples required in random sampling method, Cochran formula (1977) was used. The area was randomly allocated among Shirazi citizens. The influence of advertising on meat demand and its products was investigated using demand systems (translog, AIDS, and Rotterdam). Additionally, Excel 2013 and Stata12 were utilized to analyze the data. Results and discussion: Among the demand systems used in the present study, AIDS demand system could better express consumer behavior which was used as the optimal demand system. The attraction of advertising in the demand systems was almost ideal -0.29. According to the extent of this attraction, it can be said that to estimate AIDS demand systems, advertising could not increase the demand for goods. The coefficient obtained from advertising to estimate AIDS demand systems showed that this coefficient is negative and significant (-0.0003) and does not agree with our expectation. In other words, investing in the promotion of sausage and sausage meat products has not had a positive effect on the demand of consumers for this product. Thus, if sufficient and essential care is taken in the creation of these food items, and monitoring and control mechanisms are in place, they may play a significant part in consumers' nutrition and food baskets. The first condition to increase the demand for meat products is to gain the lost trust of people via the high-quality production of this product in compliance with hygienic principles (Bashir, 2013). Correcting advertising methods can increase the demand for this product. The effects of policies on meat and meat products are rapidly emerging (Jabarin, 2005). In terms of pricing strategies, close substitutes are very important for a product because a slight change in the price of meat leads to a shift in the demand for its products and ultimately affects the retail price level of meat products. Besides, the other dimension of this issue, namely subsidies and their reduction, must be seriously considered.
The quantity and quality of food consumed by the community are determined by the price level and household income. Household food expenditure share is still dominated by rice commodities. The aims of ...this study are 1) to analyze the level of household expenditure on food in Java and (2) to analyze the expenditure elasticity and price elasticity of household food demand in Java. The data used was March 2015, 2016, and 2017 SUSENAS data. Household consumption data was estimated using the AIDS Model. The results showed that household food expenditure share for medium and low-income groups (Q3 and Q4) for urban and rural areas was more than 50 percent. This shows that the household is food insecure. The own-price elasticity for all commodities is negative and inelastic. Changes in food prices do not significantly affect changes in demand for food commodities because their elasticity is inelastic. Household food demand is more influenced by food prices than household income for food commodities except for rice commodities. Rice has elastic expenditure elasticity (means that food demand is very responsive to changes in household expenditure/income. The relationship between each commodity is almost entirely negative (complementary).
This study focuses on an age-structured population model which describes the in host dynamics of HIV/AIDS. This model also considers the proportion of latently infected CD4+ T cells by HIV. After the ...formulation of the model, we derive steady-state solutions of the model. By constructing an appropriate Lyapunov function, we check the stability of infection-free steady-state. We show that if reproduction number R0 is less than 1, then the infection-free equilibrium is stable. We also study the role of anti-retroviral therapy to slow down the process of HIV in the human body. We consider our model with anti-retroviral therapy and again check the global stability of the infection-free steady state for better comparison. We also solve our model numerically to study the primary spread of HIV virus.
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