update README

README.md

@@ -1,3 +1,6 @@
+<center>
+<img src="https://raw.githubusercontent.com/DataForScience/epidemik/main/images/epidemik.png" /></center>
+
 # epidemik
 
 Compartmental Epidemic Models in Python
@@ -33,8 +36,9 @@ Here's a brief high-level overview of the tech stack the `epidemik` package uses
 
 - The model is implemented as a directed multigraph using [networkx](https://networkx.org/)
 - Ordinary Differential Equations are numerically integrated using [scipy](https://scipy.org/)
-- Random numbers are generated by[numpy](https://numpy.org/)
-- Model structure visualizations rely on [matplotlib](https://matplotlib.org/)  
+- Random numbers are generated by [numpy](https://numpy.org/)
+- Model structure visualizations rely on [matplotlib](https://matplotlib.org/)
+- Progress bars generated by [tqdm](https://tqdm.github.io/)
 
 
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@@ -44,13 +48,17 @@ Here's a brief high-level overview of the tech stack the `epidemik` package uses
 
 ## Usage[![](https://raw.githubusercontent.com/DataForScience/epidemik/main/images/pin.svg)](#usage)
 
-`epidemik` provides three main modules, `EpiModel`, `NetworkEpiModel` and `MetaEpiModel`, usually imported directly from the `epidemik` package using
+`epidemik` provides three main modules, `EpiModel`, `NetworkEpiModel` and `MetaEpiModel`, usually imported directly from the `epidemik` package using the module name
 
 ```python
 from epidemik import EpiModel
 ```
 
-To instanciate a new compartmental model we just need to create a `EpiModel` object and add the relevant transitions:
+- __EpiModel__ -e Simple compartmental model in a homogeneously mixed population.
+- __NetworkEpiModel__ - Compartmental model on a network where nodes interact only along edges connecting them.
+- __MetaEpiModel__ - Meta population model where populations interact with one another along the edges of a network. Each sub-population has it's own internal __EpiModel__ instance.
+
+To instantiate a new compartmental model we just need to create a `EpiModel` object and add the relevant transitions:
 
 ```python
 beta = 0.2
@@ -75,7 +83,7 @@ resulting in a simple description of hte model structure.
 
 	R0=2.00
 
-or a graphical representation by calling `draw_model`:
+or a graphical representation by calling `draw_model()`:
 
 ```python
 SIR.draw_model()
@@ -89,7 +97,9 @@ The models value of the Basic Reproductive Number (R~0~) can be determined using
 SIR.R0()
 ```
 
+There are two ways to explore the dynamics of the model, each with it's corresponding method. 
 
+To integrate numerically the Ordinary Differential Equations that describe the model dynamics, we can call the `integrate()` method. The first argument is the number of time steps to integrate over and the remaining arguments are the initial populations of each compartment.
 
 ```python
 N = 10_000
@@ -145,7 +155,7 @@ Thank you so much for your interest in growing our community!
 
 ## License[![](https://raw.githubusercontent.com/DataForScience/epidemik/main/images/pin.svg)](#license)
 
-`epidemik` is free and open-source software licensed under the [MIT License](https://choosealicense.com/licenses/mit/) [2024]  - Bruno Gonçalves. Please have a look at the [LICENSE.md](LICENSE) for more details.
+`epidemik` is free and open-source software licensed under the [MIT License](https://choosealicense.com/licenses/mit/) [2024]  - Bruno Gonçalves, Data For Science, Inc. Please have a look at the [LICENSE.md](LICENSE) for more details.
 
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