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

References

• Akyildiz, F. T., & Alshammari, F. S. (2021). Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel. Advances in Difference Equations, 53(319), 1–22. https://doi.org/10.1186/s13662-021-03470-1
   Google Scholar
• Anderson, R. (1988). The epidemiology of HIV infection: Variable incubation plus infectious periods and heterogeneity in sexual activity. With discussion. Journal of the Royal Statistical Society. Series A (Statistics in Society), 151(1), 66–98. https://doi.org/10.2307/2982185
   Google Scholar
• Arditi, R., & Ginzburg, L. R. (1989). Coupling in predator-prey dynamics: Ratio-dependence. Journal of Theoretical Biology, 139(3), 311–326. https://doi.org/10.1016/S0022-5193(89)80211-5
   Web of Science ®Google Scholar
• Bairagi, N., Roy, P., & Chattopadhyay, J. (2007). Role of infection on the stability of a predator-prey system with several response functions-a comparative study. Journal of Theoretical Biology, 248(1), 10–25. https://doi.org/10.1016/j.jtbi.2007.05.005
   PubMed Web of Science ®Google Scholar
• Biswas, S., Samanta, S., & Chattopadhyay, J. (2018). A cannibalistic eco-epidemiological model with disease in predator population. Journal of Applied Mathematics and Computing, 57(1–2), 161–197. https://doi.org/10.1142/S0218127415501308
   Web of Science ®Google Scholar
• Chiu, C. (1999). Lyapunov functions for the global stability of competing predators. Journal of Mathematical Analysis and Applications, 230(1), 232–241. https://doi.org/10.1006/jmaa.1998.6198
   Web of Science ®Google Scholar
• Dimaschko, J., Shlyakhover, V., & Labluchanskyi, M. (2021). Why did the COVID-19 epidemic stop in China and does not stop in the rest of the world? (Application of the Two-Component Model). SciMed, 3(2), 88–99. https://doi.org/10.28991/SciMedJ-2021-0302-2
   Google Scholar
• Guin, L. N. (2014). Existence of spatial patterns in a predator-prey model with self- and cross-diffusion. Applied Mathematics and Computation, 226(2014), 320–335. https://doi.org/10.1016/j.amc.2013.10.005
   Google Scholar
• Hadeler, K., & Freedman, H. (1989). Predator-prey populations with parasitic infection. Journal of Mathematical Biology, 27(6), 609–631. https://doi.org/10.1007/BF00276947
   PubMed Web of Science ®Google Scholar
• Haijiao, L., & Shangjiang, G. (2017). Dynamics of a SIRC epidemiological model. Electronic Journal of Differential Equations 2017 (121), 1–18.
   Google Scholar
• Haque, M., Ali, N., & Chakravarty, S. (2013). Study of a tri-trophic prey-dependent food chain model of interacting populations. Mathematical Biosciences, 246(1), 55–71. https://doi.org/10.1016/j.mbs.2013.07.021
   PubMed Web of Science ®Google Scholar
• Haque, M., & Venturino, E. (2007). An eco-epidemiological model with disease in predator: The ratio-dependent case. Mathematical Methods in the Applied Sciences, 30(14), 1791–1809. https://doi.org/10.1002/mma.869
   Web of Science ®Google Scholar
• Hethcote, H., Wang, W., Han, L., & Ma, Z. (2004). A predator-prey model with infected prey. Theoretical Population Biology, 66(3), 259–268. https://doi.org/10.1016/j.tpb.2004.06.010
   PubMed Web of Science ®Google Scholar
• Hsieh, Y. H., & Hsiao, C. K. (2008). Predator-prey model with disease infection in both populations. Mathematical Medicine and Biology, 25(3), 247–266. https://doi.org/10.1093/imammb/dqn017
   Web of Science ®Google Scholar
• Intissar, A. (2020). A mathematical study of a generalized SEIR model of COVID-19. SciMed, 2(2020), 30–67. https://doi.org/10.28991/SciMedJ-2020-02-SI-4
   Google Scholar
• Kermack, W., & McKendrick, A. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London, 115(772), 700–721. https://doi.org/10.1098/rspa.1927.0118
   Google Scholar
• Klempner, M. S., & Shapiro, D. S. (2004). Crossing the species barrier-one small step to man, one giant leap to mankind. New England Journal of Medicine, 12(350), 1171–1172. https://doi.org/10.1056/NEJMp048039
   Google Scholar
• Koutou, O., Traoré, B., & Sangaré, B. (2018a). Mathematical model of malaria transmission dynamics with distributed delay and a wide class of nonlinear incidence rates. Cogent Mathematics & Statistics, 5(25), 1564531. https://doi.org/10.1080/25742558.2018.1564531
   Google Scholar
• Koutou, O., Traoré, B., & Sangaré, B. (2018b). Mathematical modeling of malaria transmission global dynamics: Taking into account the immature stages of the vectors. Advances in Difference Equations, 2018(220), 34. https://doi.org/10.1186/s13662-018-1671–2
   Google Scholar
• Koutou, O., Traoré, B., & Sangaré, B. (2021). Analysis of schistosomiasis global dynamics with general incidence functions and two delays. International Journal of Applied and Computational Mathematics, 7(6), 245. https://doi.org/10.1007/s40819-021-01188-y
   Google Scholar
• Lotka, A. (1956). Elements of mathematical biology. Dover New York, 7(3), 145–214. https://doi.org/10.1002/jps.3030471044
   Google Scholar
• Mushanyu, J., Chazuka, Z., Mudzingwa, F., & Ogbogbo, C. (2021). Modelling the impact of detection on COVID-19 transmission dynamics in Ghana. Research in the Mathematical Sciences, 8(1), 1–11. https://doi.org/10.1080/27658449.2021.1953722
   Google Scholar
• Ouedraogo, H., Ouedraogo, W., & Sangaré, B. (2019). Bifurcation and stability analysis in complex cross-diffusion mathematical model of phytoplankton-fish dynamics. Journal of Partial Differential Equations, 8(3), 1–13. https://doi.org/10.4208/jpde.v32.n3.2
   Google Scholar
• Ouedraogo, H., Ouedraogo, W., & Sangaré, B. (2020). Cross and self-diffusion mathematical model with nonlinear functional response for plankton dynamics. Journal of Advanced Mathematical Studies, 13(2), 237–251.
   Google Scholar
• Rosenzweig, M. L., & MacArthur, R. (1963). Graphical representation and stability conditions of predator prey interactions. The American Naturalist, 97(895), 209–223. https://doi.org/10.1086/282272
   Web of Science ®Google Scholar
• Sarwardi, S., Haque, M., & Venturino, E. (2011). A Leslie-Gower Holling-type II ecoepidemic model. Journal of Applied Mathematics and Computing, 35(1–2), 263–280. https://doi.org/10.1007/s12190-009-0355-1
   Google Scholar
• Savadogo, A., Ouedraogo, H., Sangaré, B., & Ouedraogo, W. (2020). Mathematical analysis of a fish-plankton eco-epidemiological system. Nonlinear Studies, 27(1), 1–22.
   Google Scholar
• 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
   Google Scholar
• Subhas, K. (2017). Uniform persistence and global stability for a brain tumor and immune system interaction. Biophysical Reviews and Letters, 12(4), 1–22. https://doi.org/10.1142/S1793048017500114
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Tozzi, A., & Peters, J. F. (2019). Topology of Black Holes’ Horizons. Emerging Science Journal, 3(2), 58. https://doi.org/10.28991/esj-2019-01169
   Google Scholar
• Traoré, B., Koutou, O., & Sangaré, B. (2019). Global dynamics of a seasonal mathematical model of schistosomiasis transmission with general incidence function. Journal of Biological Systems, 27(1), 19–49. https://doi.org/10.1142/S0218339019500025
   Web of Science ®Google Scholar
• Traoré, B., Koutou, O., & Sangaré, B. (2020). A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations. Nonlinear Analysis: Real World Applications, 53(2020), 1–33. https://doi.org/10.1016/j.nonrwa.2019.103081
   Google Scholar
• Traoré, B., Sangaré, B., & Traoré, S. (2018). A mathematical model of malaria transmission in a periodic environment. Journal of Biological Dynamics, 12(1), 400–432. https://doi.org/10.1080/17513758.2018.1468935
   Web of Science ®Google Scholar
• Vidyasagar, M. (1980). Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability. IEEE Transactions on Automatic Control, 25(4), 773–779. https://doi.org/10.1109/TAC.1980.1102422
   Web of Science ®Google Scholar
• Xia, Y., Lansun, C., & Jufan, C. (1996). Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models. Computers & Mathematics with Applications, 32(4), 109–116. https://doi.org/10.1016/0898-1221(96)00129-0
   Web of Science ®Google Scholar
• Xiao, Y., & Chen, L. (2001). Modeling and analysis of a predator-prey model with disease in the prey. Mathematical Biosciences, 171(1), 59–82. https://doi.org/10.1016/s0025-5564(01)00049-9
   PubMed Web of Science ®Google Scholar
• Xiaolei, Z., Renjun, M., & Lin, W. (2020). Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries. Chaos, Solitons & Fractals, 135(2020). https://doi.org/10.1016/j.chaos.2020.109829
   Google Scholar
• Zhan, S., Shuyuan, Q., Jinfang, Y., Jianwei, Z., Sisi, S., Long, T., Jun, L., Linqi, Z., Wang, W. (2021). Bat and pangolin coronavirus spike glycoprotein structures provide insights into SARS-CoV-2 evolution. Nature Communications, 12(1607), 1–12. https://doi.org/10.1038/s41467-021–21767-3.
   Google Scholar