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Thus, since all the eigenvalues of the characteristic equation (38) have negative real part, and the local asymptotically stability of Ep is proved. G10Val OLADUILTY OF OLADUILY WGA) OF DISCAaASE PICO EQUIMIDEIUH UP Eh) OlAaAle To ensure that the cholera infection eradication is independent of initial sizes of the population of the model, it is imperative to show that the DFE of the model (1) — (3), given by Ey. is globally asymptotically stable.(GAS). To achieve this, we will use the following result introduced by (Castillo-Chevez et al, 2002). Lemma 5. (Castillo-Chevez et al., 2002) Let system (27) — (28) be written in the form:

Figure 4 Thus, since all the eigenvalues of the characteristic equation (38) have negative real part, and the local asymptotically stability of Ep is proved. G10Val OLADUILTY OF OLADUILY WGA) OF DISCAaASE PICO EQUIMIDEIUH UP Eh) OlAaAle To ensure that the cholera infection eradication is independent of initial sizes of the population of the model, it is imperative to show that the DFE of the model (1) — (3), given by Ey. is globally asymptotically stable.(GAS). To achieve this, we will use the following result introduced by (Castillo-Chevez et al, 2002). Lemma 5. (Castillo-Chevez et al., 2002) Let system (27) — (28) be written in the form:

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Figure 1: Schematic description of the mathematical model From the above assumptions, definition of variables and parameters, the interactions and flow in the different compartments are as depicted in the schematic flow diagram below.
Figure 1: Schematic description of the mathematical model From the above assumptions, definition of variables and parameters, the interactions and flow in the different compartments are as depicted in the schematic flow diagram below.
eee ee eee ee eee nn ee seen nee NN NO OE ENSIEPII! IEE IE EE NN We investigate the local stability of the disease free (DFE) state by evaluating the associated Jacobian of equations (27) — (29) at the DFE state. The Jacobian matrix J for the system (27) — (29), evaluated at the disease-free equilibrium, Ey is given by
eee ee eee ee eee nn ee seen nee NN NO OE ENSIEPII! IEE IE EE NN We investigate the local stability of the disease free (DFE) state by evaluating the associated Jacobian of equations (27) — (29) at the DFE state. The Jacobian matrix J for the system (27) — (29), evaluated at the disease-free equilibrium, Ey is given by
It is shown from Table 2, that the threshold Ro. is sensitive proportionally to the changes in the parameter values of P, @, f Table 2. Sensitivity indices of Ry
It is shown from Table 2, that the threshold Ro. is sensitive proportionally to the changes in the parameter values of P, @, f Table 2. Sensitivity indices of Ry
We show a baseline table for the parameters used in this model. The sources are also stated.
We show a baseline table for the parameters used in this model. The sources are also stated.
Figure 2: Graph of Susceptible and Infected individual in the population without control (¥ = 0,g -0,u =0,z = 0)
Figure 2: Graph of Susceptible and Infected individual in the population without control (¥ = 0,g -0,u =0,z = 0)
Figure 3: Effect of Vaccination (q = 0.03; 0.2; 0.65) of Susceptible individual without other control measures (y =¢
Figure 3: Effect of Vaccination (q = 0.03; 0.2; 0.65) of Susceptible individual without other control measures (y =¢
Figure 5: Effect of using different sanitation parameter values (Z = 0.02; 0.2; 0.7) without other control
Figure 5: Effect of using different sanitation parameter values (Z = 0.02; 0.2; 0.7) without other control
Figure 7: Graph of Susceptible and Infected individual in the population with weak controls (presence of the bacteria vibrio cholera) ¥ = 0.02;q = 0.04;u = 0.02;z = 0.02, R, < 1. Figure 7: Graph of Susceptible and Infected individual in the population with weak controls (presence of the bacteria vibrio
Figure 7: Graph of Susceptible and Infected individual in the population with weak controls (presence of the bacteria vibrio cholera) ¥ = 0.02;q = 0.04;u = 0.02;z = 0.02, R, < 1. Figure 7: Graph of Susceptible and Infected individual in the population with weak controls (presence of the bacteria vibrio
Figure 8: Graph of Susceptible and Infected individual in the population with strong controls (presence of the bacteria vibrio | —— | a =e ——
Figure 8: Graph of Susceptible and Infected individual in the population with strong controls (presence of the bacteria vibrio | —— | a =e ——
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MathematicsBiologyPublic HealthPsychological InterventionPublic health interventionsBasic Reproduction Number
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