One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this ...paper a mathematical model of fractional order is constructed to study the significance of the lockdown in mitigating the virus spread. The model consists of a system of five nonlinear fractional-order differential equations in the Caputo sense. In addition, existence and uniqueness of solutions for the fractional-order coronavirus model under lockdown are examined via the well-known Schauder and Banach fixed theorems technique, and stability analysis in the context of Ulam–Hyers and generalized Ulam–Hyers criteria is discussed. The well-known and effective numerical scheme called fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many studies recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.
To curtail and control the pandemic coronavirus (Covid-19) epidemic, there is an urgent need to understand the transmissibility of the infection. Mathematical model is an important tool to describe ...the transmission dynamics of any disease. In this research paper, we present a mathematical model consisting of a system of nonlinear fractional order differential equations, in which bats were considered as the origin of the virus that spread the disease into human population. We proved the existence and uniqueness of the solution of the model by applying Banach contraction mapping principle. The equilibrium solutions (disease free & endemic) of the model were found to be locally asymptotically stable. The key parameter (Basic reproduction number) describing the number of secondary infections was obtained. Furthermore, global stability analysis of the solutions was carried out using Lyapunov candidate function. We performed numerical simulation, which shows the changes that occur at every time instant due to the variation of α. From the graphs, we can see that FODEs have rich dynamics and are better descriptors of biological systems than traditional integer – order models.
As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that ...neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u1(t) (isolation of the susceptible communities), u2(t) (contact track measure by which susceptible individuals with contact history are quarantined), u3(t) (contact track measure by which infected individualsare quarantined), u4(t) (control effort of hospitalizing the infected I1) and u5(t) (control effort of hospitalizing the infected I2). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.
A mathematical model consisting of a system of four nonlinear ordinary differential equations is constructed. Our aim is to study the dynamics of the spread of COVID-19 in Nigeria and to show the ...effectiveness of awareness and the need for relevant authorities to engage themselves more in enlightening people on the significance of the available control measures in mitigating the spread of the disease. Two equilibrium solutions; Disease free equilibrium and Endemic equilibrium solutions were calculated and their global stability analysis was carried out. Basic reproduction ratio (
Nigeria, like most other countries in the world, imposes lockdown as a measure to curtail the spread of COVID-19. But, it is known fact that in some countries the lockdown strategy could bring the ...desired results while in some the situation could worsen the spread of the virus due to poor management and lack of facilities, palliatives and incentives. To this regard, we feel motivated to develop a new mathematical model that assesses the imposition of the lockdown in Nigeria. The model comprises of a system of five ODE. Mathematical analysis of the model were carried out, where boundedness, computation of equilibria, calculation of the basic reproduction ratio and stability analysis of the equilibria were carried out. We finally study the numerical outcomes of the governing model in respect of the approximate solutions. To this aim, we employed the effective ODE45, Euler, RK-2 and RK-4 schemes and compare the results.
In recent years, COVID-19 has evolved into many variants, posing new challenges for disease control and prevention. The Omicron variant, in particular, has been found to be highly contagious. In this ...study, we constructed and analyzed a mathematical model of COVID-19 transmission that incorporates vaccination and three different compartments of the infected population: asymptomatic Formula: see text, symptomatic Formula: see text, and Omicron Formula: see text. The model is formulated in the Caputo sense, which allows for fractional derivatives that capture the memory effects of the disease dynamics. We proved the existence and uniqueness of the solution of the model, obtained the effective reproduction number, showed that the model exhibits both endemic and disease-free equilibrium points, and showed that backward bifurcation can occur. Furthermore, we documented the effects of asymptomatic infected individuals on the disease transmission. We validated the model using real data from Thailand and found that vaccination alone is insufficient to completely eradicate the disease. We also found that Thailand must monitor asymptomatic individuals through stringent testing to halt and subsequently eradicate the disease. Our study provides novel insights into the behavior and impact of the Omicron variant and suggests possible strategies to mitigate its spread.
The emergence of highly contagious Alpha, Beta, Gamma and Delta variants and strains of COVID-19 put healthy people on high risk of contracting the infection. In addition to the vaccination ...strategies, the nonpharmaceutical intervention use of face mask gives protection against the contraction of the virus. To understand the efficacy of such, we present a Caputo type fractional dynamical model to assess the efficacy of facemask to the community transmission of COVID-19. The existence and uniqueness of the solution was established, and subsequently, with the use of the generalized mean value theorem, the positivity and boundedness of the solutions were established. The disease free equilibrium (DFE) was found to be asymptotically stable when the basic reproduction number
By constructing quadratic Lyapunov function, the equilibria (DFE and Endemic) were found to be globally asymptotically stable.
In this paper, a model that studies the effect of BCG in controlling bladder cancer is developed. This model consists of a system of three FODEs. Two equilibrium points were obtained. Existence ...uniqueness as well as the stability of the solutions of the system was given. Numerical simulations were also carried out to show the significance of the BCG in controlling bladder cancer.
Estimates of rape against women had been usually taken from two main sources till the early 1980s; The national crime victimization study and the Uniform Crime Report’s official statistics. Scholars ...argued, however, that the true incidence of rape was greatly underestimated by those data sources. For example, a uniform crime report focuses on recorded incidents, but several violations are not reported to the police. Two methodological causes have contributed to the underestimation of rape by national crime surveys. First, its definition of rape was considered too limited because it covered only carnal information and, thus, omitted many actions, such as offenses other than penile-vaginal penetration, from the scope of contemporary rape laws. Second, critics argued that the national crime survey was inappropriately structured for interviewees who had previously been assaulted to generate allegations of abuse. The crux of this critique was that there was no clear concern about rape in the national crime survey. How to establish evaluation methods that would show the real nature of rape was the crucial question. As a result of this, we are inspired to design a new mathematical model in this paper to study the dynamics of rape in our societies. Several characteristics of the established model, such as model formulation, boundedness, equilibrium solutions, basic reproduction number, global stability analysis are derived. The existence and characterization of the optimal control function are carried out. For sensitivity analysis as well as to show the significance of the control strategies, several simulation results are given. To get a deep insight into the dynamical behavior of the model, numerical simulations are performed and consequently we obtain the graphical results based on parameters taken as variables. The Euler technique is employed to do the job.
The possibility of exploiting the human immune response to glycan α-Gal for the control of multiple infectious diseases has been the objective of recent investigations. In this field of research, the ...strain of Escherichia coli O86:B7 has been at the forefront, but this Gram-negative microorganism presents a safety concern and therefore cannot be considered as a probiotic. To address this challenge, this study explored the identification of novel lactic acid bacteria with a safe history of use, producing α-Gal and having probiotic potential. The lactic acid bacteria were isolated from different traditionally fermented foods (kununn-zaki, kindirmo, and pulque) and were screened for the production of α-Gal and some specific probiotic potential indicators. The results showed that Ten (10) out of forty (40) 25% of the tested lactic acid bacteria (LAB) produced α-Gal and were identified as Limosilactobacillus fermentum, Levilactobacillus brevis, Agrilactobacillus composti, Lacticaseibacillus paracasei, Leuconostoc mesenteroides and Weissella confusa. Four (4) LAB strains with highest levels of α-Gal were further selected for in vivo study using a mouse model (α1,3GT KO mice) to elucidate the immunological response to α-Gal. The level of anti-α-Gal IgG observed were not significant while the level of anti-α-Gal IgM was lower in comparison to the level elicited by E. coli O86:B7. We concluded that the lactic acid bacteria in this study producing α-Gal have potential probiotic capacity and can be further explored in α-Gal-focused research for both the prevention and treatment of various infectious diseases and probiotic development.
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