An epidemic cholera model with control treatment and intervention

The mathematical modelling and dynamics optimization of cholera disease spread are discussed. The proposed SEIQR (Susceptible-Educated-Infected-Quarantined-Recovered) type model takes into account the bacterial concentration of the cholera spread dynamics. Three controls are considered to minimize the spread of cholera which are the treatment of quarantined populations and intervention efforts as a strategy in preventing the spread of disease through improved sanitation and education. Furthermore, the dynamics optimization problem is solved using the Pontryagin Minimum Principle method. The purpose is to decrease the populations of infected human populations and bacterial populations while minimizing the costs incurred for sanitation, educational and quarantine improvement. Numerical results are presented to show that the three controls can effectifely minimize the spread of cholera.