Stable Whenever Research Articles

Far field operator splitting and completion in inverse medium scattering

Abstract We study scattering of time-harmonic plane waves by compactly supported inhomogeneous objects in a homogeneous background medium. The far field operator associated to a fixed scatterer describes multi-static remote observations of scattered fields corresponding to arbitrary superpositions of plane wave incident fields at a single frequency. In this work we consider far field operators for systems of two well-separated scattering objects, and we discuss the nonlinear inverse problem to recover the far field operators associated to each of these two scatterers individually. This is closely related to the question whether the two components of the scatterer can be distinguished by means of inverse medium scattering in a stable way. We also study the restoration of missing or inaccurate components of an observed far field operator and comment on the benefits of far field operator splitting in this context. Both problems are ill-posed without further assumptions, but we give sufficient conditions on the diameter of the supports of the scatterers, the distance between them, and the size of the missing or corrupted data component to guarantee stable recovery whenever sufficient a priori information on the location of the unknown scatterers is available. We provide algorithms, error estimates, a stability analysis, and we demonstrate our theoretical predictions by numerical examples.

Linear and nonlinear stability of double diffusive convection in a micropolar fluid saturated porous layer with magnetic field and throughflow effects

The linear and nonlinear stability of double-diffusive convection in a porous layer saturated with micropolar fluid is examined. A transverse magnetic field is applied to the flow together with vertical throughflow. The normal mode technique is employed for linear stability analysis, whereas the energy method is used for nonlinear stability analysis. The resulting eigenvalue problems corresponding to linear and nonlinear stability theories are solved numerically by employing the bvp4c routine in MATLAB 2022(b). The critical thermal Rayleigh numbers for both linear and nonlinear analyses are computed for the different values of the governing parameters and presented graphically. A comparison is made between linear and nonlinear stability results. It is observed that the flow is more stable whenever a magnetic field is added to the flow, although the subcritical instability region also slightly increases. Increasing the Darcy number, Lewis number, coupling number, and absolute value of the throughflow parameter destabilizes the flow. On the other hand, raising the porosity of the medium and micropolar parameters stabilizes the flow. Furthermore, there is no subcritical gap in the absence of the throughflow effect, which is a good agreement between the linear and nonlinear thresholds.

Stable cartel configurations and product differentiation: The case of multiple cartels

We develop a framework to analyse stable cartelisation when firms can form multiple cartels. This contrasts with the existing literature which generally assumes, without further justification, that at most one cartel may form. We define cartelisation to be stable in the multiple cartels framework if: (i) a firm in a cartel does not find it more profitable to leave the cartel and operate independently, (ii) a firm that operates independently does not find it more profitable to join an existing cartel, (iii) a firm in a cartel does not find it more profitable to join another existing cartel or form a new cartel with an independent firm, and (iv) two independent firms do not find it more profitable to form a new cartel. In the context of quantity competition in differentiated markets, we show that a single cartel is never stable whenever multiple cartels may be formed. We completely characterise the stable cartelisation structure — there is at most one firm that is not a part of any cartel while each of the remaining firms is part of a two-firm cartel. The implication for competition policy is that efforts towards the detection of cartels should also be directed at smaller cartels that may operate in less concentrated markets rather than only on large dominant cartels in concentrated markets.

Dynamical behavior of a fractional-order epidemic model for investigating two fear effect functions

Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number Rc, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever Rc<1. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results.

Stability Analysis for Co-Dynamics of COVID-19 and HIV-AIDS with Public Sensitization and Education as Controls

Infectious diseases have denied humanity joy and resources over the centuries. Major diseases such as rabies (1885), whooping cough (1914), flu influenza (1945), and COVID-19 changed the course of life. Hence, a need for alternative methods of combating infections with optimal cost. The coronavirus has shocked the world and it was devastating. The human immunodeficiency virus (HIV) epidemic has caused individuals to rethink their sexual lives, especially in Africa, where the disease has plagued several souls. The authors developed a compartmental model for co-infection of COVID-19 and HIV infection with optimal control. The following controls were incorporated into the model: education/sensitization of susceptible populations, use of anti-retroviral therapy, treatment of co-infected populations, and treatment of the COVID-19-infected population are essential in the fight against HIV and COVID-19 infections. Qualitative and quantitative solutions to the model were determined and analyzed. The HIV-COVID-19-free equilibrium of the co-dynamics model was found to be locally asymptotically stable whenever the reproductive rate was less than one and unstable otherwise. The co-dynamic model was extended to include some controls. This was to establish which strategy is suitable for combating the spread of the COVID-19-infected population. The results of our numerical simulations revealed that in combating COVID-19 and HIV spread, education of susceptible populations and treatment of COVID-19-infected populations are the best options. There has been a reduction in COVID-19 infection, an increase in the COVID-19 recovery population, and a substantial reduction in COVID-19 populations due to this control strategy. The findings of this study are an important step in the fight against HIV and COVID-19. Hence, policymakers should place priority on public education on HIV/COVID-19 infections and treatment of the COVID-infected population when combating these diseases.

Modeling and optimal control of COVID-19 with comorbidity and three-dose vaccination in Indonesia

This paper presents and examines a COVID-19 model that takes comorbidities and up to three vaccine doses into account. We analyze the stability of the equilibria, examine herd immunity, and conduct a sensitivity analysis validated by data on COVID-19 in Indonesia. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, while an endemic equilibrium exists and is globally asymptotically stable when the number is greater than one. Subsequently, the model incorporates two effective measures, namely public education and enhanced medical care, to determine the most advantageous approach for mitigating the transmission of the disease. The optimal control model is then determined using Pontryagin’s maximum principle. The integrated control strategy is the best method for reliably safeguarding the general population against COVID-19 infection. Cost evaluations and numerical simulations corroborate this conclusion.

The use of an imperfect vaccination and awareness campaign in the control of antibiotic resistant gonorrhoea infection: A mathematical modelling perspective

The multi drug-resistant Neisseria gonorrhoeae has been classified by the World Health Organisation (WHO) as a high-priority global public health problem. This underlines the need for better understanding of the transmission dynamics and proposing an optimal intervention strategy to control the disease. In this article, a deterministic mathematical model for the transmission dynamics of gonorrhoea as an antibiotic resistant disease in a population with an imperfect vaccination is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection interventions to reduce antibiotic resistant cases. The threshold parameter R0, the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibits a backward bifurcation for R0<1. However, if the efficacy of the vaccine is 100% without a waning effect, the model is shown to be without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R0<1. The global sensitivity analysis of the model to variations in parameter values is also performed to determine the most influential parameters on the disease transmission. Moreover, the optimal control analysis of the full model is presented and the optimal intervention strategies are proposed. The proposed intervention strategies are shown to be able to control the disease within a relatively shorter period of time. Finally, numerical experiments are presented to support the theoretical analysis of the model.

Global stability analysis and modelling onchocerciasis transmission dynamics with control measures

ABSTRACT Background: Onchocerciasis infection is one of the neglected tropical diseases targeted for eradication by 2030. The disease is usually transmitted to humans through the bites of black flies. These black flies mostly breed near well-oxygenated fast-running water bodies. The disease is common in mostly remote agricultural villages near rivers and streams. Objective: In this study, a deterministic model describing the infection dynamics of human onchocerciasis disease with control measures is presented. Methods: We derived the model’s reproductive number and used a stability theorem of a Metzler matrix to show that disease-free equilibrium is both locally and globally asymptotically stable whenever the reproductive number is less than one. Parameter contribution was conducted using sensitivity analysis. The model endemic equation is shown to be a cubic polynomial in the presence of infected immigrants and a quadratic form in their absence. Results: When the inflow of infected immigrants is null, the model endemic equation may admit a unique equilibrium if the reproductive number is greater than one, or admits multiple endemic equilibria if the reproductive number is less than unity. We carried out a sensitivity analysis to identify the significant parameters that contribute to onchocerciasis spread. Conclusion: Onchocerciasis disease can be eradicated if the importation of infected immigrants is properly monitored. The integration of the One Health concept in the public health system is key in tackling the emergence and spread of diseases.

Modeling the Transmission Dynamics of Tuberculosis in Humans

Tuberculosis (TB) is a major threat to human health particularly in most of developing countries. In this article, we formulate and analyze a deterministic model for the transmission dynamics of pulmonary and extra-pulmonary tuberculosis. The next generation method is employed to find the basic reproduction number R0 which helps to determine whether TB clears or persists in the human population. Global stability of model equilibria is done through Lyapunov functions whereas the normalized forward sensitivity index method is adopted to determine parameters that drive tuberculosis. Analysis shows that both TB free and endemic equilibria exist. The TB free equilibrium is globally asymptotically stable whenever the basic reproduction number R0 &lt; 1 whereas the endemic equilibrium is globally asymptotically stable whenever R0 &gt; 1. Sensitivity analysis shows that the TB infection rate, the fraction of individuals who progress to pulmonary tuberculosis and its induced death drive TB. Numerical results indicate that when there are no interventions, susceptible humans decline significantly with time until when they are attracted to the steady state whereas latently infected, pulmonary and extra-pulmonary TB individuals increase until when they settle at the equilibrium states supporting the analytical results for existence of the endemic equilibrium. In light of these findings, we recommend treating humans infected with pulmonary TB who are carriers of the disease.

Modeling the Inflow of Exposed and Infected Migrants on the Dynamics of Malaria

Malaria is currently a life-threatening vector borne disease which is endemic in most of the developing and underdeveloped countries associated with poor health care systems. In this study, a host-vector mathematical model that takes into account the inflow of human migrants who have been exposed or infected with malaria is formulated and analysed. The reproduction number of the mosquito vector population is derived and used as a threshold quantity for determining the existence of the model trivial and realistic steady states. The Routh-Hurwitz criterion and some stability theorems of Metzler matrices are used to show that the realistic disease free equilibrium is both locally and globally asymptotically stable whenever the disease reproductive number is less than one. We derived an equation for the model endemic condition and used Descartes Rule of Sign Change to established the conditions for the model to admit one or three endemic equilibrium state(s). It is further shown that in the absence of inflow of exposed or infected migrants, the model admits a globally asymptotically unique endemic equilibrium when R0&gt;1 and two endemic equilibria when R0&lt;1. Our local sensitivity analysis revealed that the adults mosquito removal and biting rates were respectively the most significant contributing parameters to the spread of malaria. The numerical simulations results suggested that the exposed and infected immigrants have no significant impact on the dynamical behaviour of the model population sub-classes.

Transmission Dynamics of Monkeypox Virus With Age‐Structured Human Population: A Mathematical Modeling Approach

This study presents a deterministic mathematical model of monkeypox disease transmission dynamics with an age‐structured human population divided into two subgroups of children (Group 1) and adults (Group 2). Two equilibrium points, monkeypox‐free, E0, and a unique monkeypox‐endemic equilibrium point, E1, are established. The age‐structured monkeypox basic reproduction number, ℝ0, is computed using the next‐generation matrix approach and established to be ℝ0 = 1.2448. The Lyapunov functions are constructed; together with LaSalle’s invariance principle, the monkeypox‐free equilibrium point, E0, is established to be globally asymptotically stable whenever ℝ0 ≤ 1, as confirmed by the Lyapunov stability method, and the monkeypox‐endemic equilibrium point, E1, is globally asymptotically stable whenever ℝ0 &gt; 1. Sensitivity analysis of the threshold quantity ℝ0 is performed using the Latin hypercube sampling method and Pearson’s partial rank correlation coefficient, and the results showed that the parameters β11, β22, μ, ν1, Λ1, ν2 were the most sensitive to the spread of monkeypox infection in an age‐structured population. It is, therefore, suggested that the rate of monkeypox infection can be reduced by ensuring that the rate of interaction between susceptible children and infected children and between susceptible adults and infected adults is minimized. Moreover, the spread of monkeypox infection can be curbed by emphasizing controls such as early diagnosis and treatment and hospitalization of critically ill infectives.

Stability Analysis and Simulation of Diffusive Vaccinated Models

This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease’s time transmission, it is important to examine the global stability of the equilibrium points. Disease‐free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease‐free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler’s approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission.

Mathematical modeling of the effects of vector control, treatment and mass awareness on the transmission dynamics of dengue fever

Dengue fever is a vital public health concern that affects about 40% of the world’s population. To address the dynamics of dengue disease, a mathematical model was formulated by incorporating three control strategies: vector control, treatment, and mass awareness. A stability analysis of the disease-free equilibrium (DFE) was conducted using the Jacobian matrix. The DFE was found to be locally and globally asymptotically stable when the effective reproductive number was less than one; otherwise, it was unstable. Additionally, an endemic equilibrium point (EEP) was identified. The global stability analysis of the EEP, performed using the Lyapunov method, showed that it is globally asymptotically stable whenever Re>1; otherwise, it is unstable. Bifurcation analysis revealed that the model system exhibits a forward bifurcation. Furthermore, sensitivity analysis of the effective reproduction number revealed that the most sensitive parameters are the biting rate (b) and insecticide efficacy (δ). Therefore, the results suggest that, in order to reduce new dengue cases, intervention strategies that decrease the biting rate, such as mosquito repellents and the use of insecticides to kill mosquitoes, should be implemented. Moreover, simulations were conducted for the extended model with vector control, treatment, and mass awareness. The results showed that the combination of vector control, treatment, and mass awareness has a more positive impact on the control of dengue fever than any single or paired intervention. Thus, for effective control of dengue fever, the three control measures should be implemented simultaneously, especially in endemic areas.

Mathematical assessment of control strategies against the spread of MERS-CoV in humans and camels in Saudi Arabia.

A new mathematical model for the transmission dynamics and control of the Middle Eastern respiratory syndrome (MERS), a respiratory virus caused by MERS-CoV coronavirus (and primarily spread to humans by dromedary camels) that first emerged out of the Kingdom of Saudi Arabia (KSA) in 2012, was designed and used to study the transmission dynamics of the disease in a human-camel population within the KSA. Rigorous analysis of the model, which was fitted and cross-validated using the observed MERS-CoV data for the KSA, showed that its disease-free equilibrium was locally asymptotically stable whenever its reproduction number (denoted by $ {\mathbb R}_{0M} $) was less than unity. Using the fixed and estimated parameters of the model, the value of $ {\mathbb R}_{0M} $ for the KSA was estimated to be 0.84, suggesting that the prospects for MERS-CoV elimination are highly promising. The model was extended to allow for the assessment of public health intervention strategies, notably the potential use of vaccines for both humans and camels and the use of face masks by humans in public or when in close proximity with camels. Simulations of the extended model showed that the use of the face mask by humans who come in close proximity with camels, as a sole public health intervention strategy, significantly reduced human-to-camel and camel-to-human transmission of the disease, and this reduction depends on the efficacy and coverage of the mask type used in the community. For instance, if surgical masks are prioritized, the disease can be eliminated in both the human and camel population if at least 45% of individuals who have close contact with camels wear them consistently. The simulations further showed that while vaccinating humans as a sole intervention strategy only had marginal impact in reducing the disease burden in the human population, an intervention strategy based on vaccinating camels only resulted in a significant reduction in the disease burden in camels (and, consequently, in humans as well). Thus, this study suggests that attention should be focused on effectively combating the disease in the camel population, rather than in the human population. Furthermore, the extended model was used to simulate a hybrid strategy, which combined vaccination of both humans and camels as well as the use of face masks by humans. This simulation showed a marked reduction of the disease burden in both humans and camels, with an increasing effectiveness level of this intervention, in comparison to the baseline scenario or any of the aforementioned sole vaccination scenarios. In summary, this study showed that the prospect of the elimination of MERS-CoV-2 in the Kingdom of Saudi Arabia is promising using pharmaceutical (vaccination) and nonpharmaceutical (mask) intervention strategies, implemented in isolation or (preferably) in combination, that are focused on reducing the disease burden in the camel population.

Mathematical Modeling of the Transmission Dynamics of Gumboro Disease

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number Rog is derived, and the dynamical behaviors of both the disease‐free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever Rog &lt; 1 and an asymptotic stable EE whenever Rog &gt; 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings.

A MATHEMATICAL MODEL FOR TUBERCULOSIS INFECTION TRANSMISSION DYNAMICS IN THE PRESENCE OF TESTING AND THERAPY, ISOLATION AND TREATMENT

In this study, a mathematical model for Tuberculosis infection transmission dynamics is developed by incorporating testing and therapy of latent individuals, the isolation of infectious individuals and the treatment of the isolated individuals. The basic reproduction number was computed using the next generation matrix method. Analysis of the model at the disease-free equilibrium state and the endemic equilibrium states shows that it is locally and globally asymptomatically stable whenever the basic reproduction number is less than unity at the disease -free equilibrium state and locally and globally asymptotically stable whenever the basic reproduction number is greater than unity. The result from the sensitivity index of show that the infection transmission parameter and other control parameters such as early detection and therapy, the isolation of infected individuals and treatment are crucial parameters to tuberculosis management. It is shown from numerical simulations that the early detection and therapy, isolation and treatment of infected individuals will reduce the infection transmission. Further numerical results show that the combination of early detection and therapy, isolation and treatment of infectious individuals will decrease the infection transmission and its eventual eradication from the human population.

Analysis of Stability, Sensitivity Index and Hopf Bifurcation of Eco-Epidemiological SIR Model under Pesticide Application

In this paper, a deterministic SIR plant mathematical model is proposed and analysed with the application of pesticides as a control measure. The primary purpose of this model is to study the role of pesticides in controlling disease prevalence in plant populations. The total plant population is subdivided into three categories: susceptible, infected, and recovered. Pesticides are considered to be applied to both susceptible and infected populations to prevent the spread of infection to unaffected plant populations. It is considered that plant populations can be recovered only through the use of pesticides. To ensure the biological validity and well-defined nature of the model, the positivity, boundedness, uniqueness and existence of solutions are analysed. The basic reproduction number (R0) of the infection is determined and observed that the disease-free equilibrium state is locally asymptotically stable whenever (R0) is less than unity and unstable otherwise. The sensitivity analysis of the basic reproduction number is carried out, and it is observed that the value of R0 decreases as the value of the death rate and the recovery rate of plants increases. Moreover, it is revealed that above a critical parameter value of the infective induce rate, the population starts oscillating periodically, and the endemic equilibrium state becomes unstable. Finally, numerical simulations are conducted in MATLAB software to compare the analytical findings. Overall, the results obtained from this analysis are both novel and significant, making them an intriguing and potentially valuable contribution to the field of theoretical ecology.

Optimal control model for the infectiology of staphylococcus aureus with dual transmission pathways

Staphylococcus aureus has been increasing globally, which negatively affects food safety, human and veterinary medicine. It colonizes about 30% of the world population, causing superficial skin and soft tissue infections. The dynamics of direct (human-to-human) and indirect (environment-to-human) transmission, shedding, and treatment failure of the disease remains an open epidemiological challenge. Therefore, this study introduces a mathematical model that incorporates both direct and indirect transmission cycle, effect of shedding, treatment failure and time-dependent control parameters. We derive an expression for the basic reproduction number, R0s, under different scenarios. Using comparison, Lyapunov and center manifold theories, we establish that the non-optimal control model is globally asymptotically stable whenever R0s<1 with a forward bifurcation diagram. The shedding of pathogens into the environment and dual transmission routes are the key determinants in the model that increased the number of colonized individuals. Optimal control model was exploring to unveil the impact of time-dependent hygiene practice, treatment and hydrogen peroxide for good human health and clean environment. We show also the control efficacies of the proposed intervention strategies. The key finding is that having triple controls (as in strategy 7) is better than having two controls (as in strategies 4–6) or a single control (as strategies 1–3), but economically very expensive. In a situation where two controls are the only available option, then the use of either improved hygiene practice and treatment (strategy 4) or treatment and hydrogen peroxide (strategy 6) be implemented for controlling staph infection in humans and environment. Whereas, in a case only one control is affordable, then optimized treatment is better than either improved hygiene practice or hydrogen peroxide. We hope that the outcomes of this study have presented policy-makers and decision-makers of low-, middle-and high-income countries with appropriate alternative interventions to implement while dealing with staph infections.

Impact of social media on academics: a fractional order mathematical model

ABSTRACT Due to the COVID pandemic and lockdown, usage of social platforms increased for academic and non-academic purposes. As a result, students are at significant risk of developing social media addiction, so techniques to control social media addiction throughout society are required. There are several positive and negative ways in which social media affects the academic performance of a student. Most of the mathematical models exclude the past of an individual, which is critical for controlling social media consumption. Hence, this study offers a fractional-order mathematical model to analyze the impact of social media on academics. There are two equilibrium points for the proposed model: social web-free and endemic equilibrium. Based on an evaluation of the threshold value, the social web-free equilibrium point is globally asymptotically stable whenever the threshold value is less than one. Endemic equilibrium points exist when the threshold value is greater than 1. Additionally, numerical simulations have been performed to examine changes in population dynamics and validate analytical outcomes. In summary, the findings of this research reveal that social media addiction decreases as the order of the derivative decreases, demonstrating the high efficiency of a fractional-order model over an integer-order model.

Mathematical modelling of the impact of poverty on cholera outbreaks

In this paper, we propose and analyze a coupled disease‐economic model to study the impact of poverty on cholera outbreaks. We consider the stock of capital per effective units of labor, reflecting the effect of the stock of capital on cholera outbreak and transmission. The system has positive bounded solutions. We show that the disease‐free equilibrium is globally asymptotically stable whenever , while when , the disease‐free equilibrium is unstable. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. We further study various cases for the investment rate upon critical value of the investment in order to describe the effect of poverty on the infected individuals over time. The results we obtained show that increasing of the stock of capital per effective units of labor and the implementation of strategies combining awareness programs and therapeutic treatments will reduce the proportion of the infected population. To verify our analytical results, the numerical simulations on the model are performed.