Browsing by Author "Yasmin, Nusrat"

Now showing 1 - 2 of 2

Citation Count: Akram, Saima...et al. (2020). "Periodic Solutions of Some Classes of One Dimensional Non-autonomous Equation", Frontiers in Physics, Vol. 8.
Periodic Solutions of Some Classes of One Dimensional Non-autonomous Equation
(2020) Akram, Saima; Nawaz, Allah; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, the periodic solutions of a certain one-dimensional differential equation are investigated for the first order cubic non-autonomous equation. The method used here is the bifurcation of periodic solutions from a fine focus z = 0. We aimed to find the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. For classes C3, 8, C4, 3, C7, 5, C7, 6, eight periodic multiplicities have been found. To investigate the multiplicity >9, the formula for the focal value was not available in the literature. We also succeeded in constructing the formula for η10. By implementing our newly developed formula, we are able to get multiplicity ten for classes C7, 3, C9, 1, which is the highest known to date. A perturbation method has been properly established for making the maximal number of limit cycles for each class. Some examples are also presented to show the implementation of the newly developed method. By considering all of these facts, it can be concluded that the presented methods are new, authentic, and novel.
Citation Count: Akram, Saima...et al. (2020). "Standard routine techniques of modeling of tick-borne encephalitis", Open Physics, Vol. 18, No. 1, pp. 820-828.
Standard routine techniques of modeling of tick-borne encephalitis
(2020) Akram, Saima; Arooj, Aroosa; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; 56389
Tick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R 0-like threshold has been derived by using the next-generation matrix method. The formula for R 0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.