In this paper a mathematical model that analytically as well as numerically
the flow of infection disease in a population is proposed and studied. It is
assumed that the disease divided the population into five classes: immature
susceptible individuals (S1) , mature individuals (S2 ) , infectious individual
(I ), removal individuals (R) and vaccine population (V) . The existence,
uniqueness and boundedness of the solution of the model are discussed. The
local and global stability of the model is studied. Finally the global dynamics of
the proposed model is studied numerically.
In this paper, a discrete SIS epidemic model with immigrant and treatment effects is proposed. Stability analysis of the endemic equilibria and disease-free is presented. Numerical simulations are conformed the theoretical results, and it is illustrated how the immigrants, as well as treatment effects, change current model behavior
‎ Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19 pandemic ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemic has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the ep
... Show MoreA prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc
... Show MoreIn this paper, a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results
This paper proposes a new strategy to enhance the performance and accuracy of the Spiral dynamic algorithm (SDA) for use in solving real-world problems by hybridizing the SDA with the Bacterial Foraging optimization algorithm (BFA). The dynamic step size of SDA makes it a useful exploitation approach. However, it has limited exploration throughout the diversification phase, which results in getting trapped at local optima. The optimal initialization position for the SDA algorithm has been determined with the help of the chemotactic strategy of the BFA optimization algorithm, which has been utilized to improve the exploration approach of the SDA. The proposed Hybrid Adaptive Spiral Dynamic Bacterial Foraging (HASDBF)
... Show MoreThis present work is concerned with one of the syntactic issues that has been researched by many linguists, grammarians, and specialists in Islamic studies, the estimated answer to a condition. However, this topic is researched this time by examining Imam Al-Qurtbi’s opinions in interpreting related ayas from the holly Quraan in his book (Collector of Quranic Rules) or its transliteration (Al-Jami’ Li Ahkam Al-Quran). Such a step involves commenting on, tracking what Al-Qurtbi said in this regard, discussing it from the points of view of other grammarians, and judging it accordingly, taking into account the apparent surface structures of the examples collected. To achieve this objective, the inductive analytical approach has be
... Show MoreThis paper deals with two preys and stage-structured predator model with anti-predator behavior. Sufficient conditions that ensure the appearance of local and Hopf bifurcation of the system have been achieved, and it’s observed that near the free predator, the free second prey and the free first prey equilibrium points there are transcritical or pitchfork and no saddle node. While near the coexistence equilibrium point there is transcritical, pitchfork and saddle node bifurcation. For the Hopf bifurcation near the coexistence equilibrium point have been studied. Further, numerical analysis has been used to validate the main results.
In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator. e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated. e sucient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to conrm the theoretical results.