

In the analytical study of the model we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium and sensitivity analysis of the model is conducted. Analytical and numerical approach is employed to investigate the results. For the analytical analysis purpose we divided the model into two, model with vaccination and without vaccination. In this work, we consider a mathematical model of COVID-19 transmission with double-dose vaccination strategy to control the disease. The quality of the final 3D models and scenes that you would create in an application such as Blender will rely heavily on the quality of the textures you are using, to this end we have curated the top 7 websites where you can download quality PBR textures to make your rendered output as realistic as possible, totally for free, with a creative commons license (CC0).Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. To achieve this photorealistic look PBR textures normally consist of several different texture maps which include information that describes the colour of the material, its reflectiveness and roughness, the depth and height and even how the material deals with ambient lighting. For example, most metal materials will reflect a lot of light while a surface such as concrete will reflect very little light giving it a flat matt looking surface. PBR or Physically Based Rendering attempts to simulate how materials behave in the real world, particularly how they reflect and absorb light. What exactly are PBR textures and how do they help 3D artists create photorealistic images in applications such as Blender, Cinema 4D, Maya, Unity and Unreal Engine?
