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In this article, a non-integer nonlinear mathematical model for toxoplasmosis disease in human and cat population is proposed and studied. The basic concepts of the model's dynamic are given. The study of qualitative dynamics is done by the basic threshold parameter R 0 . Local and global stabilities are done and the system's disease free equilibrium point is an attractor when R 0 < 1. Besides of it, endemic equilibrium point is an attractor when R 0 > 1. The sensitivity analysis of R 0 shows which parameter has positive/negative impact on the model. Numerical simulation of the model for the parameters occurred in threshold parameter is also discussed. The techniques of Adams Bashforth Moulton will be considered to justify all the derived theoretical results which will help in understanding to study the effect of various parameters to both the transient and steady-state dynamics of the disease infection. [ABSTRACT FROM AUTHOR]

In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we prolate, the coinfection mathematical model for the implication of optimal control. Here the model (Tahir, 0004) AIDS/HIV/TB is extended for an optimal control purpose, and for sensitivity analysis of the dominant parameters involved in infection. For this purpose, initially, we apprized the threshold number of the concern model. Then the sensitivity analysis is discussed for dominant parameters which mostly spread infection in population. Moreover, simulation is shown in simple graph and area graph which shows the effected area of any population in any community by using Matlab programming. Here our mission is to minimize the coinfection problem from any community. Also we defined six control variables with different schemes to control and minimized infection. In the last section, numerical simulation is presented in a new way by Runge-Kutta method of order four, and Matlab programming which is with and without control or vaccination for the concern model. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a stochastic model for hepatitis B virus transmission with the effect of fluctuation environment. We divide the total population into four different compartments, namely, the susceptible individuals in which the disease transmission rate is distributed by white noise, the acutely infected individuals in which the same perturbation occur, the chronically infected individuals and the recovered individuals. We use the stochastic Lyapunov function theory to construct a suitable stochastic Lyapunov function for the existence of positive solution. We also then establish the sufficient conditions for the hepatitis B extinction and the hepatitis B persistence. At the end numerical simulation is carried out by using the stochastic Runge–Kutta method to support our analytical findings. [ABSTRACT FROM AUTHOR]

We propose an epidemic model for the transmission of hepatitis B virus along with the classification of different infection phases and hospitalized class. We formulate the model and discuss its basic mathematical properties, e.g. existence, positivity, and biological feasibility. Exploiting the next generation matrix approach, we find the basic reproductive number of the model. We perform sensitivity analysis to illustrate the effect of various parameters on the transmission of the disease. We investigate stability of the equilibria of the model in terms of the basic reproduction number. Conditions for the stability of the proposed model are obtained using various approaches. Finally, we perform the numerical simulations to discuss sensitivity analysis and to support our analytical work. [ABSTRACT FROM AUTHOR]

Jordan quasigroups are commutative quasigroups satisfying the identity . In this paper we discuss the basic properties of Jordan quasigroups and prove that (i) every commutative idempotent quasigroup is Jordan quasigroup, (ii) if a Jordan quasigroup Q is distributive then Q is idempotent, (iii) an idempotent entropic quasigroup satisfies Jordan's identity, (iv) a unipotent quasigroup Q satisfying Jordan's identity satisfies left nuclear square property, (vi) if a quasigroup satisfies LC identity, then alternativity ⇔ Jordan's identity, (vii) for a unipotent Jordan quasigroup Q, and (viii) every Steiner quasigroup is Jordan quasigroup. We also prove some properties of the autotopism of Jordan loops. Moreover, we construct an infinite family of nonassociative Jordan quasigroups whose smallest member is of order 6. [ABSTRACT FROM AUTHOR]

This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number R0 is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction number R0, four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies. [ABSTRACT FROM AUTHOR]

In this research article, a new mathematical delayed human immunodeficiency virus (HIV-1) infection model with two constant intracellular delays, is investigated. The analysis of the model is thoroughly discussed by the basic reproduction numbers and . For , the infection-free equilibrium is shown to be locally as well as globally stable. Similarly, the single-infection equilibrium is proved to be locally as well as globally asymptotically stable if . Our derived results show that the incorporation of even small intracellular time delay can control the spread of HIV-1 infection and can better the quality of the life of the patient. Finally, numerical simulations are used to illustrate the derived theoretical results. [ABSTRACT FROM AUTHOR]

In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically. [ABSTRACT FROM AUTHOR]

In this article, we extended the co-infection mathematical model [1] for optimal control purpose. We initially derived a threshold number R 0 and found bounded and biological region for the study of the proposed model. Here, we developed a methodology through the considered superinfection problem which is getting abate while neglecting Acquired Immuno deficiency Syndrome (AIDS) because it is a noncurable disease. For this, we developed the following control variables in our model: V 1 , using treatment against TB; V 2 , infection control in health-care center; V 3 , co-treatment of multidrug-resistant TB and HIV or start both HIV antiretroviral and anti-TB drug therapy; and V 4 , avoid close contact with TB patient. These are defined with some different schemes to minimize and control the infection from any community and population. In the last section, numerical simulation is presented which supports the given model. [ABSTRACT FROM AUTHOR]

This article discusses the Ebola virus, which is also known as Ebola haemorrhagic. Ebola virus is a transmitter virus, and the transmitting agents are wild animals, whereas in the human population it transmits from human to human. We consider the Susceptible-Exposed-Infected-Recovered (SEIR) model for our study, where the population is affected by Ebola virus by wild and domestic animals. First, we formulate the proposed model. Then, the key value, , is obtained, which is the reproductive number of the concerned model. After that, stability analyses, both local and endemic stabilities, are carried out for disease-free equilibria and endemic equilibria and we show that both are stable. Global stability at the disease-free as well as at endemic equilibrium was found to be successfully stable. For global stability at both levels, we define the Lapnuov function, finally, numerical simulation of the Runge-Kutta method is presented for the proposed model. [ABSTRACT FROM AUTHOR]

This manuscript is concerned to the existence and stability of HIV/AIDS infection model with fractional order derivative. The corresponding derivative is taken in Caputo-Fabrizio sense, which is a new approach for such type of biological models. With the help of Sumudu transform, some new results are handled. Further for the corresponding results, existence theory and uniqueness for the equilibrium solution are provided via using nonlinear functional analysis and fixed point theory due to Banach. [ABSTRACT FROM AUTHOR]