Adomian decomposition method for modelling the dissipative higher-order rogue waves in a superthermal collisional plasma

Theoretical and semi-analytical simulation for a two-predator-one-prey model during the mating period

The article introduces a new application which is a system of equations of two predators and one prey with the term of interaction between male and female of predators and prey. Such term appears when male and female of predators feed on the same prey during their mating period. The mathematical model has been studied theoretically and semi-analytically. The positivity, boundedness, local and global stability are proved for the system. The logarithm of multistage differential transform method (MsDTM) is used to study this new application. The MsDTM is used because it globally converges to the solution, it is a highly accurate, fast and simple approach. The stability analysis as well as semi-analytical solutions of the system are obtained to understand the dynamic of the model. Moreover, the effects of several parameters in the system are presented. As a results, we obtain the periodic solution when when the growth rate of prey is larger than the growth rate of both type of predators.

On fractional numerical simulation of HIV infection for CD8+ T-cells and its treatment

The AIDS is a chronic disease and the researchers still exert their high efforts to reach the cure of HIV infection. The most common treatment is the antiretroviral therapy (cART) and the virus can be more effected if the patients stop using cART. The other problem is that the CD8+ T cells might be exhausted by persistent immune activation by cART. This paper introduces fractional-order into a mathematical model of HIV infection combining with stem cell therapy and control the infection by the immune system cells (CD8+ T cells). The paper introduced the numerical solutions for the mathematical model. The results show that the stem cell therapy with the activation of immune system cells might causes the cure for a HIV patient. This results are consistent with medical studies. Also, we proposed the effect of the fractional order (α) on the figures of the components.