Dynamic study ofSIAISQVR−Bfractional-order cholera model with control strategies in Cameroon Far North Region

Abstract

Abstract In this work, mathematical S I A I S Q V R − B fractional-order cholera model is investigated. We provide a theoretical study of the model. We derive the basic reproduction number R 0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R 0 ≤ 1 , while when R 0 > 1 , the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. Using the sensitivity analysis, we find that the parameters related to the vaccination and therapeutic treatment are more influencing the model. Theoretical results are supported by numerical simulations by means of fde12 solver, which further suggest using of vaccination in endemic area. We observe from Fig. 4 that, extinction of disease can occur with vaccination of susceptible individuals for ϕ > 0.6 . In case of lack of necessary funding to fight again cholera, Fig. 3 revealed that efforts should focus to keep contamination rates σ 0.09 and β 0.09 in other to die out with success the disease.