Mathematical Modelling Study Research Articles

Potential population-level effectiveness of one-dose HPV vaccination in low-income and middle-income countries: a mathematical modelling analysis

Given the accumulating evidence that one-dose vaccination could provide high and sustained protection against human papillomavirus (HPV) infection and related diseases, we examined the population-level effectiveness and efficiency of one-dose HPV vaccination of girls compared with two-dose vaccination, using mathematical modelling. In this mathematical modelling study, we used HPV-ADVISE LMIC, an individual-based transmission-dynamic model independently calibrated to four epidemiologically diverse low-income and middle-income countries (LMICs; India, Nigeria, Uganda, and Viet Nam). We parameterised and calibrated the model using sexual behaviour and epidemiological data identified from international population-based datasets and the literature. All base-case vaccination scenarios start in 2023 with the nonavalent vaccine and assumed 80% vaccination coverage with one or two doses. We assumed that two doses of vaccine provide 100% efficacy against vaccine-type infections and a lifelong duration of protection. We examined a non-inferior vaccination scenario for one dose compared with two doses, pessimistic scenarios of lower one-dose vaccine efficacy (85%) or a shorter duration of protection (ie, 20 or 30 years), and the effectiveness of a mitigation scenario in which schedules would switch from one dose to two doses. We also did sensitivity analyses by varying vaccination coverage. We used three outcomes: the relative reduction in cervical cancer incidence, the number of cervical cancers averted, and the number of vaccine doses needed to prevent one cervical cancer. Assuming non-inferior vaccine characteristics for one dose compared with two doses, the model projections show that two-dose or one-dose routine vaccination of girls aged 9 years (with a multi-age cohort vaccination of girls aged 10-14 years) would avert 12·0 million (80% UI 9·5-14·5) cervical cancers in India, 4·7 million (3·4-5·8) in Nigeria, 2·3 million (1·9-2·6) in Uganda, and 0·4 million (0·2-0·5) in Viet Nam over 100 years. Under pessimistic assumptions of lower one-dose efficacy (85%) or a shorter duration of protection (ie, 30 years), one-dose routine vaccination would avert 69% (61-80) to 94% (92-96) of the cervical cancers averted with two-dose routine vaccination. However, when assuming a duration of protection of 20 years, one-dose routine vaccination would avert substantially fewer cervical cancers (ie, 35% [26-44] to 69% [65-71] of the cervical cancers averted with two-dose routine vaccination). A switch from one-dose to two-dose routine vaccination of girls aged 9 years, with a one-dose catch-up of girls aged 10-14 years, 5 years after the start of the vaccination programme, could mitigate potential losses in cervical cancer prevention from a short one-dose duration of protection (averting 92% [83-98] to 99% [97-100]) of the cervical cancers averted with two-dose routine vaccination). One-dose routine vaccination would result in fewer doses needed to prevent one cervical cancer than two-dose routine vaccination, even if the duration of protection is as low as 20 years. Finally, for countries with two-dose routine vaccination, adding one-dose multi-age cohort vaccination in the first year would provide similar benefits as a two-dose multi-age cohort vaccination, and would be more efficient even under the pessimistic assumptions of lower one-dose vaccine efficacy or duration of protection. One-dose routine vaccination could avert most of the cervical cancers averted with two-dose vaccination while being more efficient, provided the duration of one-dose protection is greater than 20-30 years (depending on the LMIC). The doses saved by introducing one-dose routine vaccination could offer the opportunity to vaccinate girls before they age out of the vaccination window of 9-14 years and, potentially, to vaccinate boys or older age groups. Fonds de recherche du Québec-Santé, Digital Research Alliance of Canada, Bill & Melinda Gates Foundation.

A numerical study of a new non-linear fractal fractional mathematical model of malicious codes propagation in wireless sensor networks

This paper presents a novel non-linear fractal fractional mathematical model for analyzing the spread of malicious codes in wireless sensor networks (WSNs). The model incorporates fractional calculus and non-linear interactions among nodes in a WSN. It is based on the Fractal-Fractional (FF) operator, a powerful mathematical tool that combines fractional and fractal calculus. This study explores the potential of fractional derivatives in addressing computer virus-related issues and proposes a model that elucidates the spread of viruses in a vulnerable system and potential countermeasures. The Fractal-Fractional operator is utilized to fractionalize the model, and the fixed point theory of Schauder and Banach is applied to establish the existence and uniqueness of a solution. Numerical simulations, employing MATLAB and the Adams-Bashforth method, validate the effectiveness of the proposed model in capturing the propagation dynamics of malicious codes. Ulam-Hyers stability techniques are also employed for stability analysis. The model's insights contribute to enhancing the security and robustness of WSNs against malicious code propagation, paving the way for more secure network designs. This research provides a unique perspective on analyzing the dynamics of WSNs and underscores the significance of fractional derivatives in addressing security threats in network systems.

Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading

The notion of prosumers, people who create and consume energy, has emerged in the energy sector as a result of the fast integration of renewable energy sources and advances in digital technology. Platforms for peer-to-peer (P2P) energy trading have come to light as viable ways to allow prosumers to conduct direct energy transactions within small groups. Existing P2P trading models, however, frequently lack an optimized approach to maximize the advantages for prosumers. In this article, we provide a novel six-segment strategy (SSS) that is intended to increase prosumers′ ability to maximize their benefits in P2P energy trading systems. Additionally, the SSS promotes prosumers′ active market engagement by supporting community-driven energy exchanges. Through extensive mathematical modeling, simulations, and case studies, we demonstrate the effectiveness of the six-segment strategy in enhancing the economic benefits of prosumers participating in P2P energy trading. The proposed optimization strategy holds the potential to revolutionize the energy landscape by promoting more sustainable and consumer-centric energy trading. The cost savings of 12.9% are distributed among prosumers by the SSS, which is an improvement compared with previously proposed strategies.

Appearance of chaos and bi-stability in a fear induced delayed predator–prey system: A mathematical modeling study

Since many years ago, it has been only a priori assumption that the diversity of ecological demography is largely influenced by the direct interactions of predator and prey species. But over the years, it has also been recognized that an indirect effect can also affect the system more strongly. The effect of fear on prey species is that it restricts physical activities and feeding times of prey thereby reducing interactions with their predators and leading to an intraspecific competition among predators. By these motives, we investigate a delay-induced model inducing fear of predators on the prey population. Existence of feasible steady points, well posedness of the solutions, local & global stability, subcritical & supercritical bifurcation are well presented. The results show that predator fear reduces both prey and predator populations, but does not affect the steady state of the system. As delay increases within a specific range, it changes the dynamics of the system in a stable–unstable–stable sequences. A small delay shifts an unstable interior equilibrium to a predator-free stable equilibrium. The main result of this study is that a large delay produces chaotic dynamics when cost of fear is high and prey birth is low, whereas a small delay creates bi-stable dynamics when cost of fear is low and prey birth is high. Furthermore, by increasing the competitiveness among the predators, the chaos can be completely controlled. We examine that small fear has a greater effect while relatively large fear has less effect. Delay parameter is responsible for appearing stability switch more than once. Extensive numerical simulations are also carried out for various parameters.

Transmission dynamics and effect of control measures on the 2022 outbreak of mpox among gay, bisexual, and other men who have sex with men in England: a mathematical modelling study

The 2022 global outbreak of mpox (formerly known as monkeypox) spread primarily among gay, bisexual, and other men who have sex with men (GBMSM), with the initial cluster being identified in England in May, 2022. Understanding its epidemiological characteristics and the reasons for its downturn in July, 2022, will help to control future outbreaks. We collated data for all diagnosed mpox cases (3621) from England from May 1, 2022, to Nov 16, 2022. Data from 75 individuals with mpox allowed estimation of the incubation period, while data from 121 case-contact pairs were used to estimate the serial interval. Six methods, including a structured dynamic compartmental transmission model, were used to estimate the basic reproduction number (R0). The structured model assumed all male individuals with mpox were GBMSM, who were then stratified into subgroups for those at low risk and high risk for mpox. This best fitting model was used to estimate the reduction in transmissibility, and the effective infectious period (before isolating), that resulted in the outbreak downturn, and the effect of vaccination initiated from June 27, 2022. Bayesian methods were used for parameter estimation and model calibration. Most cases occurred in men (3544 of 3621, 97·9%). The median incubation period for mpox was 6·90 days (95% credible interval [CrI] 4·08-20·21), and the serial interval was 8·82 days (5·22-25·81). R0 estimates ranged from 1·41 to 2·17. The structured transmission model estimated that 83·8% of infections (95% CrI 83·5-85·3) resulted from sexual partnerships with GBMSM individuals at high risk of mpox. The outbreak downturn probably resulted from a 44·5% reduction in the sexual partner rate among all GBMSM (24·9-55·8) and 20·0% reduction in the effective infectious period (4·1-33·9), preventing 165 896 infections (115 584-217 730). Vaccination marginally increased the number of infections prevented (166 081, 115 745-217 947), but minimised a resurgence in cases from January, 2023, and could have averted four times more infections if initiated earlier. Our findings were sensitive to assumptions regarding the vaccine's effectiveness and the GBMSM subgroup at high risk of mpox. The mpox outbreak in England probably resulted from high sexual partner rates among some GBMSM, with reductions in partner rates reversing the outbreak, and with vaccination minimising future outbreaks. National Institute for Health Research (UK).

Assessing the potential impact of COVID-19 booster doses and oral antivirals: A mathematical modelling study of selected middle-income countries in the Indo-Pacific

Continued efforts to reduce the burden of COVID-19 require the consideration of additional booster doses and emerging oral antivirals. This study explored the individual- and population-level impacts of booster dose and oral antivirals in Indonesia, Fiji, Papua New Guinea, and Timor-Leste. Our mathematical model included age structure, vaccine coverage, prevalence of comorbidities, and immunity from prior infection fit to incidence data from our study settings. We explored a range of eligibility criteria and found that boosters had the largest impact per dose when prioritised to high-risk adults and adults who had not previously received a booster. Antivirals were most effective in settings with low vaccine-derived immunity. In general, fewer antivirals than booster doses were required to prevent a hospitalisation or death. Only in settings with very high vaccine uptake was the impact per dose of providing booster doses to high-risk adults comparable to providing oral antivirals to high-risk adults. Together, booster doses and oral antivirals could prevent 80%, 64%, 49%, and 65% of deaths, and 38%, 37%, 16%, and 34% of hospitalisations in Fiji, Indonesia, Papua New Guinea, and Timor-Leste respectively. Therefore, our findings support the continued provision of COVID-19 booster doses to high-risk adults in 2023, and advocate for increased access to oral antivirals, especially in settings with low vaccine coverage such as Papua New Guinea. Future work should consider the threshold at which self-financing of COVID-19 oral antivirals would be viable for middle-income countries in South-East Asia and the Pacific.

Maternal vaccination against RSV can substantially reduce childhood mortality in low-income and middle-income countries: A mathematical modeling study

BackgroundRespiratory syncytial virus (RSV) is a leading cause of childhood mortality in infants below 6 months of age. In low-income and middle-income countries (LMICs), the public health burden is substantial and resources are limited. It is critical to inform decision makers about effectiveness of new interventions. MethodsWe developed a mathematical model where individual RSV subtype A (RSV-A) and B (RSV-B) maternally derived neutralizing titers were predicted at time of birth after maternal vaccination with the RSV prefusion F protein-based vaccine. We estimated the subsequent duration of vaccine-induced immunity and compared this to the age at time of death distribution in the RSV GOLD Mortality Database to predict the potential impact of maternal vaccination on RSV-related childhood mortality. We used country-specific timing of antenatal care visits distributions and mortality estimates to make country-specific predictions for number of cases averted. FindingsThe model predicts that on average a neonate born at 40 weeks gestational age will be protected between 6 and 7 months from RSV-A and approximately 5 months from RSV-B related mortality. We estimated the potential impact of RSV-related mortality for in-hospital and out-of-hospital cases in LMICs and predicted that in 51 GAVI-eligible countries maternal vaccination could avert between 55% and 63% of the RSV-related in-hospital mortality cases below 6 months of age. InterpretationWe show that maternal vaccination could substantially decrease RSV-A and RSV-B related in-hospital and out-of-hospital mortality in LMICs in the first 6 months of life.

Результаты мониторинга интеграции учебных дисциплин в условиях цифрового образования

The authors study the problem of implementing integrative links between academic disciplines at an economic university using digital tools. The importance of digital technologies as a means of integration for the study of economic and mathematical models in the process of mathematical training of students of an economic university is determined. A practical problem is considered, demonstrating the constructive possibilities of economic and mathematical modeling and digital tools in the implementation of integrative links between academic disciplines. When solving the problem, a double integral is used as a mathematical model, which makes it possible to formalize and study the socio-economic process. The capabilities of the Python programming language, which provides the implementation of an intra-model solution, are demonstrated. In the course of the study, the authors monitored the dynamics of the level of integrative connections of academic disciplines within the framework of the continuity of educational programs for undergraduate and graduate programs. An online survey was conducted among students of an enlarged group of areas of training in Economics and Management on the problematic aspects of using digital tools to study economic and mathematical models and obtain integrated educational results. The findings indicate the need for further development of integrative links between the disciplines of the subject areas “Economics”, “Mathematics”, “Computer Science and Information Technology” in the context of digital education, which, in turn, provides the necessary level of quality of modern educational results.

Analisis Bibliometrik Trend Penelitian Pemodelan Matematis Menggunakan Database Google Scholar, Publish or Perish, dan Vosviewer

This study aims to identify the topic of the study of mathematical modeling by highlighting publications on Google Scholar from 1951 to 2022. This study uses the Google Scholar citation database for 71 years to collect articles. The keyword used in this research is "mathematical modeling" with a filter of English documents. Simple statistical methods were used, and bibliometric analysis was performed using Publish or Perish and Vos-viewer software. This study visualizes the co-occurrence patterns of keywords and citations. This study reveals a significant research trend in the field of mathematical modeling from 71 years ago. Based on the visualization of the large cluster network map which includes mathematical modeling concepts, it is known that the health sector is dominant as the background for its presence. Study of the topic of mathematical modeling still revolves around theoretical developments, economics, industry and environment. However, there has been no study of mathematical modeling in the social and cultural fields. Moreover, by using the bibliometric method to re-identify keywords that are in accordance with the development of problem solving through mathematical models

Resistance-minimising strategies for introducing a novel antibiotic for gonorrhoea treatment: a mathematical modelling study

Gonorrhoea is a highly prevalent sexually transmitted infection and an urgent public health concern because of increasing antibiotic resistance in Neisseria gonorrhoeae. Only ceftriaxone remains as the recommended treatment in the USA. With the prospect of new anti-gonococcal antibiotics being approved, we aimed to evaluate how to deploy a new drug to maximise its clinically useful lifespan. We used a compartmental model of gonorrhoea transmission in a US population of men who have sex with men (MSM) to compare strategies for introducing a new antibiotic for gonorrhoea treatment. The MSM population was stratified into three sexual activity groups (low, intermediate, and high) characterised by annual rates of partner change. The four introduction strategies tested were: (1) random 50-50 allocation, where each treatment-seeking infected individual had a 50% probability of receiving either drug A (current drug; a ceftriaxone-like antibiotic) or drug B (a new antibiotic), effective at time 0; (2) combination therapy of both the current drug and the new antibiotic; (3) reserve strategy, by which the new antibiotic was held in reserve until the current therapy reached a 5% threshold prevalence of resistance; and (4) gradual switch, or the gradual introduction of the new drug until random 50-50 allocation was reached. The primary outcome of interest was the time until 5% prevalence of resistance to each of the drugs (the new drug and the current ceftriaxone-like antibiotic); sensitivity of the primary outcome to the properties of the new antibiotic, specifically the probability of resistance emergence after treatment and the fitness costs of resistance, was explored. Secondary outcomes included the time to a 1% resistance threshold for each drug, as well as population-level prevalence, mean and range annual incidence, and the cumulative number of incident gonococcal infections. Under baseline model conditions, a 5% prevalence of resistance to each of drugs A and B was reached within 13·9 years with the reserve strategy, 18·2 years with the gradual switch strategy, 19·2 years with the random 50-50 allocation strategy, and 19·9 years with the combination therapy strategy. The reserve strategy was consistently inferior for mitigating antibiotic resistance under the parameter space explored and was increasingly outperformed by the other strategies as the probability of de novo resistance emergence decreased and as the fitness costs associated with resistance increased. Combination therapy tended to prolong the development of antibiotic resistance and minimise the number of annual gonococcal infections (under baseline model conditions, mean number of incident infections per year 178 641 [range 177 998-181 731] with combination therapy, 180 084 [178 011-184 405] with the reserve strategy). Our study argues for rapid introduction of new anti-gonococcal antibiotics, recognising that the feasibility of each strategy must incorporate cost, safety, and other practical concerns. The analyses should be revisited once robust estimates of key parameters-ie, the likelihood of emergence of resistance and fitness costs of resistance for the new antibiotic-are available. US Centers for Disease Control and Prevention, National Institute of Allergy and Infectious Diseases.

Study of fractional-order alcohol-abuse mathematical model using the concept of piecewise operator

In this paper, we study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under some advanced concept of fractional derivative called piecewise fractional-order derivative. Currently, most real-world problems are considered under fractional derivatives because of their stable and global behavior. To deal with and detect the crossover behavior in the dynamics of the proposed model, the piecewise derivative containing the Mittag-Leffler-type kernel combined with classical integer order derivatives in piecewise form is used. First, we will investigate the model for qualitative theory in detail. For qualitative theory, we will use fixed point theory. Additionally, we establish sufficient conditions for Ulam–Hyers (UH) stability. To simulate the model, we develop a numerical algorithm based on the Euler technique. The numerical method is applied to present graphically the approximate solutions of the model. In the final part of the paper, we give a detailed discussion of our numerical results.

A data-driven Markov process for infectious disease transmission.

The 2019 coronavirus pandemic exudes public health and socio-economic burden globally, raising an unprecedented concern for infectious diseases. Thus, describing the infectious disease transmission process to design effective intervention measures and restrict its spread is a critical scientific issue. We propose a level-dependent Markov model with infinite state space to characterize viral disorders like COVID-19. The levels and states in this model represent the stages of outbreak development and the possible number of infectious disease patients. The transfer of states between levels reflects the explosive transmission process of infectious disease. A simulation method with heterogeneous infection is proposed to solve the model rapidly. After that, simulation experiments were conducted using MATLAB according to the reported data on COVID-19 published by Johns Hopkins. Comparing the simulation results with the actual situation shows that our proposed model can well capture the transmission dynamics of infectious diseases with and without imposed interventions and evaluate the effectiveness of intervention strategies. Further, the influence of model parameters on transmission dynamics is analyzed, which helps to develop reasonable intervention strategies. The proposed approach extends the theoretical study of mathematical modeling of infectious diseases and contributes to developing models that can describe an infinite number of infected persons.

Evolutionary computational method for tuberculosis model with fuzziness

This work investigates the computational study of a six-compartmental mathematical model of tuberculosis disease dynamics with the impact of vaccination. Traditional mathematical models presume that all variables are precise and can be measured or calculated precisely. However, in many real-world scenarios, variables may need to be more accurate or easier to quantify, resulting in model uncertainty. Considering this, fuzziness is introduced into the model by taking the contact, recovery, and death rates due to disease as fuzzy membership functions. Two numerical computational schemes, forward Euler and nonstandard finite difference (NSFD), are designed to solve the model. The positivity and convergence for the developed method are investigated, which are significant characteristics of these dynamical models, and it is revealed that these features are preserved in the extended scheme. Numerical computations are performed to support the analytical results. The numerical and computational results indicate that the proposed NSFD method adequately represents the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to design and develop control strategies to support decision-making.

Epidemiological Characteristics of Generalized COVID-19 Deterministic Disease Model

Coronavirus disease 2019 (COVID-19) is an infection that can result in lung issues such as pneumonia and, in extreme situations, the most severe acute respiratory syndrome. COVID-19 is widely investigated by researchers through mathematical models from different aspects. Inspired from the literature, in the present paper, the generalized deterministic COVID-19 model is considered and examined. The basic reproduction number is obtained which is a key factor in defining the nonlinear dynamics of biological and physical obstacles in the study of mathematical models of COVID-19 disease. To better comprehend the dynamical behavior of the continuous model, two unconditionally stable schemes, i.e., mixed Euler and nonstandard finite difference (NSFD) schemes are developed for the continuous model. For the discrete NSFD scheme, the boundedness and positivity of solutions are discussed in detail. The local stability of disease-free and endemic equilibria is demonstrated by constructing Jacobian matrices for NSFD scheme; nevertheless, the global stability of aforementioned equilibria is verified by using Lyapunov functions. Numerical simulations are also presented that demonstrate how both the schemes are effective and suitable for solving the continuous model. Consequently, the outcomes obtained through these schemes are completely according to the solutions of the continuous model.

Double Diffusive Convective Flow Study of a Hybrid Nanofluid in an Inverted T-Shaped Porous Enclosure Under the Influence of Soret and Dufour Prameters

Abstract This study presents a numerical investigation to examine the influence of Soret and Dufour parameters on the double-diffusive convective flow of a hybrid nanofluid within an inverted T-shaped porous enclosure. The thermophysical properties and numerical values of the hybrid nanofluid are adopted from experimentally published data. The mathematical model is formulated based on the generalized Darcy–Brinkmann–Forchheimer equation and subsequently simulated using the penalty finite element method. A parametric study is conducted, encompassing a wide range of parameters for Rayleigh number, Darcy number, porosity value, buoyancy ratio, Lewis number, Soret parameter, and Dufour parameter. The resulting flow patterns, temperature distribution (isotherms), and concentration distribution (isoconcentration plots) provide insights into the fluid flow, heat transfer, and mass transfer phenomena within the physical domain. Furthermore, the heat and mass transfer rates at the heated (concentrated) wall are quantitatively evaluated by the mean Nusselt number and mean Sherwood number, respectively, considering various combinations of flow parameters. As a key finding, it is observed that the smaller value of the Rayleigh number remains insignificant at convective flow of thermal and solute phenomena. Moreover, the higher value of Ra reinforces the convective strength of hybrid nanofluid, and it helps to identify the real impact of each parameter. Thus, at a higher Rayleigh number, it is observed that the increasing value of Darcy number, porosity value, Lewis number, and buoyancy ratio significantly influence the convective flow of heat and solute transport activity, whereas the impact of Soret and Dufour parameters shows a relatively less influence on the heat and mass transfer phenomena.

Mathematical Modelling of Transmission of Covid-19 in Indian Context: An Impact of Lockdown

Mathematical Modelling study has been carried out to model the out spread of Covid-19 in a localized society of India. Based on the transmission mechanism of Covid-19 authors established dynamics model of six chambers with population birth rate and mortality. Ordinary differential equations are used to model the system mathematically and solved numerically using ODE23 scheme. India imposes lockdown in very early stage of the Covid-19 transmission and impact of lockdown has been discussed through the mathematical model. Parameters are considered in view of the March scenario in India and the impact we got is quite similar with the present situation.

On the similarity between aortic and carotid pressure diastolic decay: a mathematical modelling study

Aortic diastolic pressure decay (DPD) has been shown to have considerable pathophysiological relevance in the assessment of vascular health, as it is significantly affected by arterial stiffening. Nonetheless, the aortic pressure waveform is rarely available and hence the utility of the aortic DPD is limited. On the other hand, carotid blood pressure is often used as a surrogate of central (aortic) blood pressure in cardiovascular monitoring. Although the two waveforms are inherently different, it is unknown whether the aortic DPD shares a common pattern with the carotid DPD. In this study, we compared the DPD time constant of the aorta (aortic RC) and the DPD time constant of the carotid artery (carotid RC) using an in-silico-generated healthy population from a previously validated one-dimensional numerical model of the arterial tree. Our results demonstrated that there is near-absolute agreement between the aortic RC and the carotid RC. In particular, a correlation of ~ 1 was reported for a distribution of aortic/carotid RC values equal to 1.76 ± 0.94 s/1.74 ± 0.87 s. To the best of our knowledge, this is the first study to compare the DPD of the aortic and the carotid pressure waveform. The findings indicate a strong correlation between carotid DPD and aortic DPD, supported by the examination of curve shape and the diastolic decay time constant across a wide range of simulated cardiovascular conditions. Additional investigation is required to validate these results in human subjects and assess their applicability in vivo.

Assessing required SARS-CoV-2 blanket testing rates for possible control of the outbreak in the epicentre Lusaka province of Zambia with consideration for asymptomatic individuals: A simple mathematical modelling study (lay summary) 

Assessing required SARS-CoV-2 blanket testing rates for possible control of the outbreak in the epicentre Lusaka province of Zambia with consideration for asymptomatic individuals: A simple mathematical modelling study (lay summary) 

Multiple solutions in magnetohydrodynamic stagnation flow of hybrid nanofluid past a sheet with mathematical chemical reactions model and stability analysis

The homogeneous heterogeneous reactions (H–H reactions) in the magnetohydrodynamic (MHD) boundary layer stagnated flow of an Al2O3–Cu–water base hybrid nanofluid past a stretching shrinking sheet are studied. A newly developed two-phase hybrid nanofluid model based on Buongiorno's model is used to understand the nanofluids behaviors. Multiple solutions are observed for specific ranges of various parameters, whose stabilities are checked and discussed, which seem to have been neglected in previously published articles about studies of MHD-stagnation flow and mathematical chemical reactions models using hybrid nanofluid. The heterogeneous reaction considered in this case is isothermal and first order, whereas the homogeneous chemical reaction is isothermal cubic autocatalytic. The solutions so captured are examined using various graphs to demonstrate the impact of different physical parameters, and their physical insights are also given. The results show that hybrid nanofluids, which have distinct functions in the processes of homogeneous and heterogeneous reactions, play a key role in the homogeneous–heterogeneous reactions' transport mechanism. The quadratic multiple regression analysis evaluations of the local Nusselt number demonstrate that the thermophoretic impact predominates over Brownian motion for both magnetic and non-magnetic effects.

Development of the structure and methodological support of the system for analysis of the details shaping using the technological inheritability of their quality parameters

Theoretical approaches, computer modell methods and experimental studies analyse the state and behaviour of machine parts to determine the changes in their properties and parameters from a single synergetic position. Development and implementation of integrated information systems for control of technological processes of manufacturing parts and machines assembly is an essential mover of the economic growth of industrialized countries. Complicating the operational conditions for the products increases the requirements for the parameters of their accuracy, surface layer quality, performance characteristics and reliability indicators. A mechanical engineering product is a technical system consisting of many subsystems and using the functionally-oriented design of technological processes planning for parts manufacturing. The structure and methodological providing of the PSPAS-system (Product Shaping / Processing Analysis System) investigates. PSPAS system includes the investigations of the technological inheritability of mechanical engineering product quality parameters combined with the analysis of traditional subsystems (cutting, surface plastic deformation, surface layer modification, assembly). Rheological simulation modelling, holding of experimental studies, the combination of mathematical modelling, theoretical and practical studies of technological processes ensure the implementation of the CAF system using the principle of functionally-oriented design during parts manufacturing and machines assembly.