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    An investigation of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system: Lie symmetry reductions, invariant solutions, dynamical behaviors and conservation laws
    (Elsevier, 2022) Kumar, Sachin; Kumar, Amit; Inc, Mustafa; Alotaibi, Hammad; Abdou, M. A.; Akguel, Ali
    In this study, we develop the asymmetric Nizhnik-Novikov-Veselov (ANNV) system in (2+1)-dimensions, which has applications in processes of interaction of exponentially localized wave structures, as well as the infinitesimal generators, Lie symmetries, vector fields, and the commutator table. The link between Lie symmetry vectors and conserved vectors is constructed using symmetry conservation principles once Lie point symmetries are first deduced. Using the aforementioned Lie symmetry technique, two-stage symmetry reductions are used to obtain the precise analytical answers. These analytical solutions all incorporate a number of different functional parameters as well as arbitrary constant parameters. The diversity of the physical phenomena of the obtained soliton solutions is illustrated by the inclusion of arbitraryness of functional parameters and constants. By using Noether's method, conservation laws have subsequently been attained. The innovative aspect of the work described in this paper is an attempt to use 3-dimensional and 2-dimensional visuals, along with appropriate arbitrary parameter selections and functional parameter values, to represent the dynamical behavior of the solutions that have been produced. In order to make this research more intriguing, stripe solitons, dark-bright solitons, solitary waves, singular wave-form soliton, and other types of soliton wave profiles of the achieved solutions are described. The effectiveness, benefits, and utility of the employed approach are demonstrated by the physical and graphical interpretation of the answers attained.
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    Öğe
    Cholera disease dynamics with vaccination control using delay differential equation
    (Nature Portfolio, 2024) Singh, Jaskirat Pal; Kumar, Sachin; Akgul, Ali; Hassani, Murad Khan
    The COVID-19 pandemic came with many setbacks, be it to a country's economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.