Joec-Tech/Malaria_Model_Bayelsa

This model is a simple malaria describing the transmission dynamics of malaria in Bayelsa, Nigeria # Compartmental Modelling for Malaria in Brass LGA This repository contains a compartmental model for simulating and analyzing malaria incidence in Brass LGA, Bayelsa State, Nigeria. ## Project Objectives This project aims to: 1. Develop a mathematical model of malaria transmission. 2. Solve the model using numerical techniques. 3. Fit the model to real-world malaria incidence data. 4. Provide clear descriptions of the model compartments and parameters. ## Model Equation The dynamics of the human and mosquito populations are governed by the following system of differential equations: $$ \frac{dS_h}{dt} = \Lambda_h - \frac{\beta_h S_h I_m}{N_m} + \alpha_h R_h $$ $$ \frac{dI_h}{dt} = \frac{\beta_h S_h I_m}{N_m} - \gamma_h I_h $$ $$ \frac{dR_h}{dt} = \gamma_h I_h - \alpha_h R_h $$ $$ \frac{dS_m}{dt} = \Lambda_m - \frac{\beta_m S_m I_h}{N_h} - \mu_m S_m $$ $$ \frac{dI_m}{dt} = \frac{\beta_m S_m I_h}{N_h} - \mu_m I_m $$ ## Model Description The model is a compartmental SIR-based model with two interacting populations: humans and mosquitoes. ### Human Compartments: - $S_h$: Susceptible humans - $I_h$: Infected humans - $R_h$: Recovered humans ### Mosquito Compartments: - $S_m$: Susceptible mosquitoes - $I_m$: Infected mosquitoes ### Incidence: - $Inc$: Cumulative incidence in humans ## Assumptions - Human lifespan is long; human mortality is neglected. - Malaria-related human deaths are negligible. - Mosquito-to-human population ratio is 200:1. - Equal initial infection proportion in both populations. - Mosquito population remains constant. ## Time Unit - The unit of time used in the simulation is 1 month (30 days). ## Parameter Classification - **Known parameters** (from demographic or biological assumptions): - $μ_m$, $λ_m$, $λ_h$, $γ_h$ - **Unknown parameters** (estimated via curve fitting): - $β_h$, $α_h$, $β_m$ ## Files in This Repository - `Data.txt`: Input incidence data - `malaria_model.py` or `.ipynb`: Model implementation and fitting - …