Mathematical Model For Transmission Research Articles

Assessing the impact of preventative measures to limit the spread of Toxoplasma gondii in wild carnivores of Madagascar.

Novel multihost pathogens can threaten endangered wildlife species, as well as humans and domestic animals. The zoonotic protozoan parasite Toxoplasma gondii is transmitted by members of Felidae and can infect a large number of animal species, including humans. This parasite can have significant health consequences for infected intermediate hosts and could further endanger wild carnivore populations of Madagascar. Building on an empirical characterization of the prevalence of the pathogen in local mammals, we used mathematical models of pathogen transmission in a multihost community to compare preventative measures that aim to limit the spread of this parasite in wild carnivores. Specifically, we examined the effect of hypothetical cat vaccination and population control campaigns on reducing the risk of infection by T. gondii in wild Eupleridae. Our model predicted that the prevalence of exposure to T. gondii in cats would be around 72% and that seroprevalence would reach 2% and 43% in rodents and wild carnivores, respectively. Reducing the rodent population in the landscape by half may only decrease the prevalence of T. gondii in carnivores by 10%. Similarly, cat vaccination and reducing the population of definitive hosts had limited impact on the prevalence of T. gondii in wild carnivorans of Madagascar. A significant reduction in prevalence would require extremely high vaccination, low turnover, or both in the cat population. Other potential control methods of T. gondii in endangered Eupleridae include targeted vaccination of wild animals but would require further investigation. Eliminating the threat entirely will be difficult because of the ubiquity of cats and the persistence of the parasite in the environment.

Construction of the mathematical model of magnetic transmission for an autonomous wind power plant

Construction of the mathematical model of magnetic transmission for an autonomous wind power plant

The impact of quality-adjusted life years on evaluating COVID-19 mitigation strategies: lessons from age-specific vaccination roll-out and variants of concern in Belgium (2020-2022)

BackgroundWhen formulating and evaluating COVID-19 vaccination strategies, an emphasis has been placed on preventing severe disease that overburdens healthcare systems and leads to mortality. However, more conventional outcomes such as quality-adjusted life years (QALYs) and inequality indicators are warranted as additional information for policymakers.MethodsWe adopted a mathematical transmission model to describe the infectious disease dynamics of SARS-COV-2, including disease mortality and morbidity, and to evaluate (non)pharmaceutical interventions. Therefore, we considered temporal immunity levels, together with the distinct transmissibility of variants of concern (VOCs) and their corresponding vaccine effectiveness. We included both general and age-specific characteristics related to SARS-CoV-2 vaccination. Our scenario study is informed by data from Belgium, focusing on the period from August 2021 until February 2022, when vaccination for children aged 5-11 years was initially not yet licensed and first booster doses were administered to adults. More specifically, we investigated the potential impact of an earlier vaccination programme for children and increased or reduced historical adult booster dose uptake.ResultsThrough simulations, we demonstrate that increasing vaccine uptake in children aged 5-11 years in August–September 2021 could have led to reduced disease incidence and ICU occupancy, which was an essential indicator for implementing non-pharmaceutical interventions and maintaining healthcare system functionality. However, an enhanced booster dose regimen for adults from November 2021 onward could have resulted in more substantial cumulative QALY gains, particularly through the prevention of elevated levels of infection and disease incidence associated with the emergence of Omicron VOC. In both scenarios, the need for non-pharmaceutical interventions could have decreased, potentially boosting economic activity and mental well-being.ConclusionsWhen calculating the impact of measures to mitigate disease spread in terms of life years lost due to COVID-19 mortality, we highlight the impact of COVID-19 on the health-related quality of life of survivors. Our study underscores that disease-related morbidity could constitute a significant part of the overall health burden. Our quantitative findings depend on the specific setup of the interventions under review, which is open to debate or should be contextualised within future situations.

Clutch model for focal adhesions predicts reduced self-stabilization under oblique pulling

Cell-matrix adhesions connect the cytoskeleton to the extracellular environment and are essential for maintaining the integrity of tissue and whole organisms. Remarkably, cell adhesions can adapt their size and composition to an applied force such that their size and strength increases proportionally to the load. Mathematical models for the clutch-like force transmission at adhesions are frequently based on the assumption that mechanical load is applied tangentially to the adhesion plane. Recently, we suggested a molecular mechanism that can explain adhesion growth under load for planar cell adhesions. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which for thermodynamic reasons, leads to the association of further molecules with the cluster, which we refer to as self-stabilization. Here, we generalize this model to forces that pull at an oblique angle to the plane supporting the cell, and examine if this idealized model also predicts self-stabilization. We also allow for a variable distance between the parallel planes representing cytoskeletal F-actin and transmembrane integrins. Simulation results demonstrate that the binding mechanism and the geometry of the cluster have a strong influence on the response of adhesion clusters to force. For oblique angles smaller than about 40∘, we observe a growth of the adhesion site under force. However this self-stabilization is reduced as the angle between the force and substrate plane increases, with vanishing self-stabilization for normal pulling. Overall, these results highlight the fundamental difference between the assumption of pulling and shearing forces in commonly used models of cell adhesion.

Utilizing direct and indirect information to improve the COVID-19 vaccination booster scheduling

Current global COVID-19 booster scheduling strategies mainly focus on vaccinating high-risk populations at predetermined intervals. However, these strategies overlook key data: the direct insights into individual immunity levels from active serological testing and the indirect information available either through sample-based sero-surveillance, or vital demographic, location, and epidemiological factors. Our research, employing an age-, risk-, and region-structured mathematical model of disease transmission—based on COVID-19 incidence and vaccination data from Israel between 15 May 2020 and 25 October 2021—reveals that a more comprehensive strategy integrating these elements can significantly reduce COVID-19 hospitalizations without increasing existing booster coverage. Notably, the effective use of indirect information alone can considerably decrease COVID-19 cases and hospitalizations, without the need for additional vaccine doses. This approach may also be applicable in optimizing vaccination strategies for other infectious diseases, including influenza.

Cost-effectiveness and public health impact of typhoid conjugate vaccine introduction strategies in Bangladesh

PurposeTyphoid fever causes substantial morbidity and mortality in Bangladesh. The government of Bangladesh plans to introduce typhoid conjugate vaccines (TCV) in its expanded program on immunization (EPI) schedule. However, the optimal introduction strategy in addition to the costs and benefits of such a program are unclear. MethodsWe extended an existing mathematical model of typhoid transmission to integrate cost data, clinical incidence data, and recently conducted serosurveys in urban, semi-urban, and rural areas. In our primary analysis, we evaluated the status quo (i.e., no vaccination) and eight vaccine introduction strategies including routine and 1-time campaign strategies, which differed by age groups targeted and geographic focus. Model outcomes included clinical incidence, seroincidence, deaths, costs, disability-adjusted life years (DALYs), and incremental cost-effectiveness ratios (ICERs) for each strategy. We adopted a societal perspective, 10-year model time horizon, and 3 % annual discount rate. We performed probabilistic, one-way, and scenario sensitivity analyses including adopting a healthcare perspective and alternate model time horizons. ResultsWe projected that all TCV strategies would be cost saving compared to the status quo. The preferred strategy was a nationwide introduction of TCV at 9–12 months of age with a single catch-up campaign for children ages 1–15, which was cost saving compared to all other strategies and the status quo. In the 10 years following implementation, we projected this strategy would avert 3.77 million cases (95 % CrI: 2.60 – 5.18), 11.31 thousand deaths (95 % CrI: 3.77 – 23.60), and save $172.35 million (95 % CrI: −14.29 – 460.59) compared to the status quo. Our findings were broadly robust to changes in parameter values and willingness-to-pay thresholds. ConclusionsWe projected that nationwide TCV introduction with a catch-up campaign would substantially reduce typhoid incidence and very likely be cost saving in Bangladesh.

Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives

This study delves into the dynamics of Zika virus transmission by employing a mathematical model to explain virus spread with fractional order derivatives. The population is divided into two groups: the human group and the ticks group to accurately explain the transmission routes of the virus. The objective of this research is to protect susceptible individuals from infection and curb the spread of this endemic disease. To achieve this, we have included two control measures: the first is a sensibilization program, and the second is treatment. We investigate the use of optimal control strategies and fractional derivative techniques under the Caputo method to reduce the number of exposed and infected individuals. By employing the Pontryagin maximum principle to analyze and characterize the optimal controls, the proposed method is further validated through numerical simulations. The outcome of this study highlights the importance of containing the rate of dynamic dissemination in preventing the Zika epidemic.

A Mathematical Model for Transmission of Taeniasis and Neurocysticercosis

In this study, we present a mathematical model for the codynamics of taeniasis and neurocysticercosis and rigorously analyze it. To understand the underlying dynamics of the proposed model, basic system properties such as the positivity and boundedness of solutions are investigated through the completing differential process. The basic reproduction number was calculated using the next-generation matrix method, and the analysis showed that when R0<1, the disease in the community eventually dies out, and when R0>1, the diseases persist. Local stability of the equilibria was analyzed using the Jacobian matrix, and Lyapunov function techniques were used to determine the global analysis, which showed that the endemic equilibrium point was globally stable when R0>1. On the other hand, the disease-free equilibrium was determined to be globally stable when R0<1. To identify the most influential parameters of the proposed model, partial correlation coefficient techniques were used. The numerical results depict that the model aligns well with the transmission dynamics, which goes through two populations: humans and pigs, whereby the model system stabilizes after some time, showing the validity of the proposed model. Furthermore, the simulations of the proposed model revealed that the shedding habit of infected humans with taeniasis and the bad cooking habit or eating of raw or undercooked pork products have a higher impact on the spread of neurocysticercosis and taeniasis in the community. Hence, this study proposes that in order to control taeniasis and neurocysticercosis, effective disease control measures should primarily prioritize hygienic behaviour and proper cooking of pork meat to the required temperature.

A study on Chlamydia transmission in United States through the Haar wavelet technique

In this study, a novel method known as the Haar wavelet collocation method (HWCM) is used to analyze the mathematical model of Chlamydia transmission in the United States. We use dependent variables with various parameters, such as birth rate, mortality rate, and recovery rate, etc., to explore the nature of the Chlamydia disease in susceptible unvaccinated individuals, susceptible vaccinated individuals, infected, treated, and recovered individuals. The ordinary differential equations (ODEs) in this model are coupled nonlinear. In this method, the Chlamydia model is converted into a system of non-linear algebraic equations using properties of the operational matrix of Haar wavelets. Later, the Newton–Raphson approach is used to extract the unknown coefficients. Mathematica software has been used for all calculations. Tables and graphs contain tabulated results of calculations. As a result, it can be seen that the current approach is more precise than those used in the literature. Also, we discuss the effect of different parameters on susceptible unvaccinated individuals, susceptible vaccinated individuals, infected, treated, and recovered individuals through graphs.

The public health impact and cost-effectiveness of the R21/Matrix-M malaria vaccine: a mathematical modelling study

The R21/Matrix-M vaccine has demonstrated high efficacy against Plasmodium falciparum clinical malaria in children in sub-Saharan Africa. Using trial data, we aimed to estimate the public health impact and cost-effectiveness of vaccine introduction across sub-Saharan Africa. We fitted a semi-mechanistic model of the relationship between anti-circumsporozoite protein antibody titres and vaccine efficacy to data from 3 years of follow-up in the phase 2b trial of R21/Matrix-M in Nanoro, Burkina Faso. We validated the model by comparing predicted vaccine efficacy to that observed over 12-18 months in the phase 3 trial. Integrating this framework within a mathematical transmission model, we estimated the cases, malaria deaths, and disability-adjusted life-years (DALYs) averted and cost-effectiveness over a 15-year time horizon across a range of transmission settings in sub-Saharan Africa. Cost-effectiveness was estimated incorporating the cost of vaccine introduction (dose, consumables, and delivery) relative to existing interventions at baseline. We report estimates at a median of 20% parasite prevalence in children aged 2-10 years (PfPR2-10) and ranges from 3% to 65% PfPR2-10. Anti-circumsporozoite protein antibody titres were found to satisfy the criteria for a surrogate of protection for vaccine efficacy against clinical malaria. Age-based implementation of a four-dose regimen of R21/Matrix-M vaccine was estimated to avert 181 825 (range 38 815-333 491) clinical cases per 100 000 fully vaccinated children in perennial settings and 202 017 (29 868-405 702) clinical cases per 100 000 fully vaccinated children in seasonal settings. Similar estimates were obtained for seasonal or hybrid implementation. Under an assumed vaccine dose price of US$3, the incremental cost per clinical case averted was $7 (range 4-48) in perennial settings and $6 (3-63) in seasonal settings and the incremental cost per DALY averted was $34 (29-139) in perennial settings and $30 (22-172) in seasonal settings, with lower cost-effectiveness ratios in settings with higher PfPR2-10. Introduction of the R21/Matrix-M malaria vaccine could have a substantial public health benefit across sub-Saharan Africa. The Wellcome Trust, the Bill & Melinda Gates Foundation, the UK Medical Research Council, the European and Developing Countries Clinical Trials Partnership 2 and 3, the NIHR Oxford Biomedical Research Centre, and the Serum Institute of India, Open Philanthropy.

Modeling resource allocation strategies for insecticide-treated bed nets to achieve malaria eradication

Large reductions in the global malaria burden have been achieved, but plateauing funding poses a challenge for progressing towards the ultimate goal of malaria eradication. Using previously published mathematical models of Plasmodium falciparum and Plasmodium vivax transmission incorporating insecticide-treated nets (ITNs) as an illustrative intervention, we sought to identify the global funding allocation that maximized impact under defined objectives and across a range of global funding budgets. The optimal strategy for case reduction mirrored an allocation framework that prioritizes funding for high-transmission settings, resulting in total case reductions of 76% and 66% at intermediate budget levels, respectively. Allocation strategies that had the greatest impact on case reductions were associated with lesser near-term impacts on the global population at risk. The optimal funding distribution prioritized high ITN coverage in high-transmission settings endemic for P. falciparum only, while maintaining lower levels in low-transmission settings. However, at high budgets, 62% of funding was targeted to low-transmission settings co-endemic for P. falciparum and P. vivax. These results support current global strategies to prioritize funding to high-burden P. falciparum-endemic settings in sub-Saharan Africa to minimize clinical malaria burden and progress towards elimination, but highlight a trade-off with ‘shrinking the map’ through a focus on near-elimination settings and addressing the burden of P. vivax.

Modeling resource allocation strategies for insecticide-treated bed nets to achieve malaria eradication.

Large reductions in the global malaria burden have been achieved, but plateauing funding poses a challenge for progressing towards the ultimate goal of malaria eradication. Using previously published mathematical models of Plasmodium falciparum and Plasmodium vivax transmission incorporating insecticide-treated nets (ITNs) as an illustrative intervention, we sought to identify the global funding allocation that maximized impact under defined objectives and across a range of global funding budgets. The optimal strategy for case reduction mirrored an allocation framework that prioritizes funding for high-transmission settings, resulting in total case reductions of 76% and 66% at intermediate budget levels, respectively. Allocation strategies that had the greatest impact on case reductions were associated with lesser near-term impacts on the global population at risk. The optimal funding distribution prioritized high ITN coverage in high-transmission settings endemic for P. falciparum only, while maintaining lower levels in low-transmission settings. However, at high budgets, 62% of funding was targeted to low-transmission settings co-endemic for P. falciparum and P. vivax. These results support current global strategies to prioritize funding to high-burden P. falciparum-endemic settings in sub-Saharan Africa to minimize clinical malaria burden and progress towards elimination, but highlight a trade-off with 'shrinking the map' through a focus on near-elimination settings and addressing the burden of P. vivax.

Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution’s uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (γ) and fractal dimensions (θ), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models.

Counterfactual analysis of the 2023 Omicron XBB wave in China

BackgroundChina has experienced a COVID-19 wave caused by Omicron XBB variant starting in April 2023. Our aim is to conduct a retrospective analysis exploring the dynamics of the outbreak under counterfactual scenarios that combine the use of vaccines, antiviral drugs, and nonpharmaceutical interventions. MethodsWe developed a mathematical model of XBB transmission in China, which has been calibrated using SARS-CoV-2 positive rates per week. Intrinsic age-specific infection-hospitalization risk, infection-ICU risk, and infection-fatality risk were used to estimate disease burdens, characterized as number of hospital admissions, ICU admissions, and deaths. ResultsWe estimated that in absence of behavioral change, the XBB outbreak in spring 2023 would have resulted in 0.86 billion infections (∼61% of the total population). Our counterfactual analysis shows that the synergetic effect of vaccination (70% vaccination coverage), antiviral treatment (20% receiving antiviral treatment), and moderate nonpharmaceutical interventions (20% isolation and L1 PHSMs) could reduce the number of deaths to levels close to seasonal influenza (1.17 vs. 0.65 per 10,000 individuals and 5.85 vs. 3.85 per 10,000 individuals aged 60+, respectively). The maximum peak prevalence of hospital and ICU admissions are estimated to be lower than the corresponding capacities (8.6 vs. 10.4 per 10,000 individuals and 1.2 vs. 2.1 per 10,000 individuals, respectively). ConclusionOur findings suggest that the capacity of the Chinese healthcare system was adequate to face the Omicron XBB wave in spring 2023 but, at the same time, supports the importance of administering highly effective vaccine with long-lasting immune response, and the use of antiviral treatments.

Backward bifurcation of a plant virus dynamics model with nonlinear continuous and impulsive control.

Roguing and elimination of vectors are the most commonly seen biological control strategies regarding the spread of plant viruses. It is practically significant to establish the mathematical models of plant virus transmission and regard the effect of removing infected plants as well as eliminating vector strategies on plant virus eradication. We proposed the mathematical models of plant virus transmission with nonlinear continuous and pulse removal of infected plants and vectors. In terms of the nonlinear continuous control strategy, the threshold values of the existence and stability of multiple equilibria have been provided. Moreover, the conditions for the occurrence of backward bifurcation were also provided. Regarding the nonlinear impulsive control strategy, the stability of the disease-free periodic solution and the threshold of the persistence of the disease were given. With the application of the fixed point theory, the conditions for the existence of forward and backward bifurcations of the model were presented. Our results demonstrated that there was a backward bifurcation phenomenon in continuous systems, and there was also a backward bifurcation phenomenon in impulsive control systems. Moreover, we found that removing healthy plants increased the threshold $ R_{1}. $ Finally, numerical simulation was employed to verify our conclusions.

Parameters estimation of a mathematical model of COVID-19 transmission in East Java Province using the deep learning method

Parameters estimation of a mathematical model of COVID-19 transmission in East Java Province using the deep learning method

Mathematical Modeling of Giardiasis Transmission Dynamics with Control Strategies in the Presence of Carriers

Giardiasis is among the ignored zoonotic illnesses accorded by the World Health Organization that is caused by Giardia duodenalis. The disease is ignored regardless of the harm it causes to people and other creatures. In this paper, a mathematical model for giardiasis illness transmission is formed, which considers sickness carriers and control measures such as screening, treatment, and sanitation of the environment around people. In the assessment, the basic reproduction number, R 0 , which is used for analyzing the local stability of the equilibria is determined using the state-of-the-art next-generation matrix, while the Metzler constancy speculation is used to show the overall adequacy of the global stability of the equilibrium point free from the disease. In addition, a Lyapunov function has been used to study the stability of the endemic equilibrium point. The assessment of parameters is performed to explore the limits that significantly influence the transmission components of the disease disorders using the normalizing sensitivity index method. The result revealed that the recruitment rate is the most sensitive limit to the reproduction number. The environment-human interaction parameter is the second influential factor in the transmission of giardiasis in the community. In the same manner, the outcomes recommend that carriers assume an expected part in the rate of giardiasis subsequently; disregarding them could risk endeavors to control the pestilence. Besides, the mathematical recreation of the model shows that a mix of each of the three interventions fundamentally affects the control of giardiasis. In this way, we advise implementing the strategies simultaneously in endemic areas to effectively stop the spread of the giardiasis disease in humans.

Population-level effectiveness of pre-exposure prophylaxis for HIV prevention among men who have sex with men in Montréal (Canada): a modelling study of surveillance and survey data.

HIV pre-exposure prophylaxis (PrEP) has been recommended and partly subsidized in Québec, Canada, since 2013. We evaluated the population-level impact of PrEP on HIV transmission among men who have sex with men (MSM) in Montréal, Québec's largest city, over 2013-2021. We used an agent-based mathematical model of sexual HIV transmission to estimate the fraction of HIV acquisitions averted by PrEP compared to a counterfactual scenario without PrEP. The model was calibrated to local MSM survey, surveillance, and cohort data and accounted for COVID-19 pandemic impacts on sexual activity, HIV prevention, and care. PrEP was modelled from 2013 onwards, assuming 86% individual-level effectiveness. The PrEP eligibility criteria were: any anal sex unprotected by condoms (past 6 months) and either multiple partnerships (past 6 months) or multiple uses of post-exposure prophylaxis (lifetime). To assess potential optimization strategies, we modelled hypothetical scenarios prioritizing PrEP to MSM with high sexual activity (≥11 anal sex partners annually) or aged ⩽45 years, increasing coverage to levels achieved in Vancouver, Canada (where PrEP is free-of-charge), and improving retention. Over 2013-2021, the estimated annual HIV incidence decreased from 0.4 (90% credible interval [CrI]: 0.3-0.6) to 0.2 (90% CrI: 0.1-0.2) per 100 person-years. PrEP coverage among HIV-negative MSM remained low until 2015 (<1%). Afterwards, coverage increased to a maximum of 10% of all HIV-negative MSM, or about 16% of the 62% PrEP-eligible HIV-negative MSM in 2020. Over 2015-2021, PrEP averted an estimated 20% (90% CrI: 11%-30%) of cumulative HIV acquisitions. The hypothetical scenarios modelled showed that, at the same coverage level, prioritizing PrEP to high sexual activity MSM could have averted 30% (90% CrI: 19%-42%) of HIV acquisitions from 2015-2021. Even larger impacts could have resulted from higher coverage. Under the provincial eligibility criteria, reaching 10% coverage among HIV-negative MSM in 2015 and 30% in 2019, like attained in Vancouver, could have averted up to 63% (90% CrI: 54%-70%) of HIV acquisitions from 2015 to 2021. PrEP reduced population-level HIV transmission among Montréal MSM. However, our study suggests missed prevention opportunities and adds support for public policies that reduce PrEP barriers, financial or otherwise, to MSM at risk of HIV acquisition.

СОВЕРШЕНСТВОВАНИЕ АКУСТИЧЕСКОГО ПОВЕДЕНИЯ КОРПУСА АВТОМАТИЧЕСКОЙ КОРОБКИ ПЕРЕДАЧ АВТОМОБИЛЯ КАТЕГОРИИ N2 НА ОСНОВЕ МЕТОДА МОДАЛЬНОГО ПРЕДСТАВЛЕНИЯ ДИНАМИЧЕСКОЙ СИСТЕМЫ

There is a global tendency nowadays in the development of transport vehicles to ensure high safety, energy efficiency and comfort, characterized primarily by ergonomic and vibroacoustic indicators. This forces engineers and scientists to constantly strive to reduce a noise level emitted by both the vehicle as a whole and individual units and systems. The paper is a continuation of a series of articles devoted to the development of a verified mathematical model of a promising automatic transmission (AT) for a N2 category vehicle, reliably characterizing its vibroacoustic behavior. The article represents the results of a computational and experimental study of the AT vibroacoustic behavior, including the stages of testing, processing and analysis of their results, verification of the computational model created in the Simcenter 3D software product, identification of the main sources of acoustic radiation and the development of proposals for its reduction. The vibroacoustic characteristics of the object of study are obtained, namely frequencies and corresponding acoustic pressure values, their localization on the AT housing is performed. The developed and verified AT model makes it possible to predict the level of vibration and acoustic radiation with satisfactory accuracy. Based on comparative evaluation modeling of various design modification options, the best ones are determined, which allow to obtain the minimum acoustic pressure level at the measurement points and neutralize the most significant forms of vibrations. The introduction of the developed scientifically-based technical solutions into the design made it possible to reduce the integral level of acoustic pressure in the entire range from 2 to 10 dBA.

A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

In this paper, we present a mathematical model for the transmission of hantavirus among rodents and its effect on the number of hantavirus-infected human population. We investigate the model and present a standard analysis in mathematical epidemiology, such as determining the equilibria of the system and their stability analysis, together with the relationship to the basic reproduction number. It is found that the endemic equilibrium exists and is locally asymptotically stable when the basic reproduction number is greater than one; otherwise, the disease-free equilibrium is stable. Later on, we also show that by constructing a suitable Lyapunov function, the endemic equilibrium is globally asymptotically stable whenever it exists. Based on the basic reproduction number, we present a critical level of intervention to control the spread of the disease to humans. We found a significant finding from the present model that if the basic reproduction number is greater than one, then it is impossible to completely eliminate hantavirus disease in the system by solely focusing on any intervention for humans, like vaccination and curative action, without paying any attention to interventions for rodent populations. However, we can still decrease the density of infected humans with those interventions. Hence, we suggest that a combination of several interventions is needed to obtain effective control in eliminating the hantavirus. This information is useful for further study in finding an optimal control strategy to reduce or eliminate the transmission of hantavirus to humans.