| Abstract: | The computational techniques are a set of novel problem-solving methodologies that have attracted wider attention for their excellent performance. The handling strategies of real-world problems are artificial neural networks (ANN), evolutionary computing (EC), and many more. An estimated fifty thousand to ninety thousand new leishmaniasis cases occur annually, with only 25% to 45% reported to the World Health Organization (WHO). It remains one of the top parasitic diseases with outbreak and mortality potential. In 2020, more than ninety percent of new cases reported to World Health Organization (WHO) occurred in ten countries: Brazil, China, Ethiopia, Eritrea, India, Kenya, Somalia, South Sudan, Sudan, and Yemen. The transmission of visceral leishmaniasis is studied dynamically and numerically. The study included positivity, boundedness, equilibria, reproduction number, and local stability of the model in the dynamical analysis. Some detailed methods like Runge Kutta and Euler depend on time steps and violate the physical relevance of the disease. They produce negative and unbounded results, so in disease dynamics, such developments have no biological significance; in other words, these results are meaningless. But the implicit nonstandard finite difference method does not depend on time step, positive, bounded, dynamic and consistent. All the computational techniques and their results were compared using computer simulations. |
