Mathematical modelling and numerical simulations of the influence of hygiene and seasons on the spread of cholera.

•The intra-annual variations of climate (temperature and rainfall) are proposed.•The impact of climatic factors and socio-economic factors on the spread of cholera are investigated.•The dynamic of disease is modeled by non-autonomous ordinary differential equations.•The extinction and uniform persistence of disease was investigated as function of two thresholds make that depend on the intra-annual variations of climate and level of education.•Numerical simulations have been carried out.