Dynamic Study of SIQR-B Fractional-Order Epidemic Model of Cholera with Optimal Control Strategies in Mayo-Tsanaga Department of Cameroon Far North Region
Abstract
In this paper, we investigated the dynamical behavior of a fractional-order model of the cholera epidemic in Mayo-Tsanaga Department. We extended the model of Lemos-Paião et al. [A. P. Lemos-Paião, C. J. Silva and D. F. M. Torres, J. Comput. Appl. Math.16, 427 (2016)] by incorporating the contact rate σσ by handling cholera death and optimal control strategies such as vaccination vv, water sanitation ww. We provide a theoretical study of the model. We derive the basic reproduction number ℛ0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever ℛ0≤1, while when ℛ0>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 parameter related to vaccination and therapeutic treatment is more influencing the model. Theoretical results are supported by numerical simulations, which further suggest use of vaccination in endemic area. In case of a lack of necessary funding to fight again cholera, Figure 6 revealed that efforts should focus to keep contamination rate σ<0.24 (susceptible-to-cholera death) in other to die out the disease.
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