A mathematical analysis of prey-predator population dynamics in the presence of an SIS infectious disease

Figures & data

Figure 1. Interaction diagram for the prey-predator model.

Figure 2. Interaction diagram for the prey-predator model when the disease spreads in the two populations.

Figure 3. Global asymptotic stability of the coexisting equilibrium $E_3$ of model (2).

Table 1. Parameters values used for the numerical simulation of system (2)

Parameters	Values	References
$r_1$	1.0009	estimated
$r_2$	0.9000001	estimated
$K_1$	250	Savadogo et al. (2021) and Tewa et al. (2013)
$K_2$	90	Savadogo et al. (2021) and Tewa et al. (2013)
$k_1$	1.00089	estimated
$k_2$	0.00111594	estimated
$\omega$	0.08010099	estimated

Figure 4. Local asymptotic stability of the coexisting equilibrium of system (2) corresponding to $k_1=1.8$.

Figure 5. Dynamics of the trajectories of model (2) with periodic solutions with $k_{1c}=1.89$.

Figure 6. Global asymptotic stability of the coexisting equilibrium $E_5$ of model (5) when $R_{02}=6.11>1$ and $R_{03}=1.33>1$.

Table 2. Parameters values used for the numerical simulation of system (5)

Parameters	Values	References
$r_1$	1.8	Savadogo et al. (2021)
$r_2$	0.0123	estimated
$K_1$	350	estimated
$K_2$	100	estimated
$k_1$	1.01	estimated
$k_2$	0.0221	estimated
$\omega$	0.1	Savadogo et al. (2021) and Tewa et al. (2013)
${\beta }_1$	1.59	estimated
${\beta }_2$	1.59	estimated
${\sigma }_1$	0.15	Tewa et al. (2013)
${\sigma }_2$	0.15	Savadogo et al. (2021) and Tewa et al. (2013)
${\theta }_1$	0.89	estimated
${\theta }_2$	0.5	estimated
${\mu }_1$	0.05	estimated
${\mu }_2$	0.05	estimated
$\delta$	0.05	estimated

Figure 7. Local asymptotic stability of the coexisting equilibrium $E_5$ of model (5) corresponding to $k_1=1.1$ with $R_{02}=6.11>1$, $R_{03}=1.41>1$.

Figure 8. Hopf-bifurcation of system (5) with persistence of disease in two populations population corresponding to $k_1=1.2$ with $R_{03}=1.42>1$.

Savadogo, A., Sangaré, B., & Ouedraogo, H. (2021). A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response. Advances in Difference Equations, 400(275), 1–23. https://doi.org/10.1186/s13662-021-03437-2

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Tewa, J. J., Djeumen, V. Y., & Bowong, S. (2013). Predator–prey model with holling response function of type II and SIS infectious disease. Applied Mathematical Modelling, 37(7), 47–57. https://doi.org/10.1016/j.apm.2012.10.003

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