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, $R_0$, 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.

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.

In this subsection, we presented a mathematical model of Ebola virus (EBOV) proposed by susceptible exposed infected recovered (SEIR) model. In our model, the population is affected by animals. EBOV is an infectious agent causing haemorraghic fever, a severe infectious disease characterised by high fever and bleeding, in humans and some monkeys. Here, we assessed the transmissibility associated with the infection stages of EBOV that generated an epidemic model. In order to do this, in the first step, we formulate the model, and the basic properties of the proposed model are presented. The basic reproductive number is obtained by using the next generation matrix approach. Then, all the endemic equilibrium points related to the disease are derived. We also find the conditions to investigate all possible equilibria of the model in terms of the basic reproduction number (local and global stability). In last, numerical simulation is presented with and without vaccination or control for the proposed model.

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.