Wolbachia invasion to wild mosquito population in stochastic environment. (English) Zbl 1530.92319
Summary: Releasing Wolbachia-infected mosquitoes to invade the wild mosquito population is a method of mosquito control. In this paper, a stochastic mosquito population model with Wolbachia invasion perturbed by environmental fluctuation is studied. Firstly, the well-posedness, positivity, and Markov-Feller property of the solution for this model are proved. Then a group of sharp threshold-type conditions is provided to characterize the long-term behavior of the model, which pinpoints the almost necessary and sufficient conditions for the persistence and extinction of Wolbachia-infected and uninfected mosquito populations. Our results indicate that even for a low initial Wolbachia infection frequency, a successful Wolbachia invasion into the wild mosquito population can be driven by stochastic environmental fluctuations. Finally, some numerical experiments are carried out to support our theoretical results.
Keywords:
mosquito population model; Wolbachia; stochastic environment; permanence; extinction; stationary distributionReferences:
| [1] | Ai, S.; Li, J.; Yu, J.; Zheng, B., Stage-structured models for interactive wild and periodically and impulsively released sterile mosquitoes. Discrete Contin. Dyn. Syst., Ser. B, 3039-3053 (2022) · Zbl 1500.34035 |
| [2] | Baldacchino, F.; Caputo, B.; Chandre, F.; Drago, A.; Alessandra, T.; Montarsi, F.; Drago, A.; della Torre, A.; Montarsi, F.; Rizzoli, A., Control methods against invasive Aedes mosquitoes in Europe: a review. Pest Manag. Sci., 1471-1485 (2015) |
| [3] | Bao, J.; Shao, J., Permanence and extinction of regime-switching predator-prey models. SIAM J. Math. Anal., 725-739 (2016) · Zbl 1337.60147 |
| [4] | Benaïm, M.; Schreiber, S. J., Persistence and extinction for stochastic ecological models with internal and external variables. J. Math. Biol., 393-431 (2019) · Zbl 1417.92207 |
| [5] | Calisher, C. H., Persistent emergence of dengue. Emerg. Infect. Dis., 738-739 (2005) |
| [6] | Caspari, E.; Watson, G. S., On the evolutionary importance of cytoplasmic sterility in mosquitoes. Evolution, 568-570 (1959) |
| [7] | Couret, J.; Dotson, E.; Benedict, M. Q., Temperature, larval diet, and density effects on development rate and survival of Aedes aegypti (Diptera: Culicidae). PLoS ONE (2014) |
| [8] | Da Prato, G.; Zabczyk, J., Ergodicity for Infinite-Dimensional Systems (1996), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0849.60052 |
| [9] | Evans, S. N.; Hening, A.; Schreiber, S. J., Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments. J. Math. Biol., 325-359 (2015) · Zbl 1322.92057 |
| [10] | Hemingway, J.; Ranson, H., Insecticide resistance in insect vectors of human disease. Annu. Rev. Entomol., 371-391 (2000) |
| [11] | Hening, A.; Nguyen, D. H., Coexistence and extinction for stochastic Kolmogorov systems. Ann. Appl. Probab., 1893-1942 (2018) · Zbl 1410.60094 |
| [12] | Hening, A.; Nguyen, D. H., Stochastic Lotka-Volterra food chains. J. Math. Biol., 135-163 (2018) · Zbl 1392.92075 |
| [13] | Hoffmann, A. A.; Montgomery, B. L.; Popovici, J.; Iturbe-Ormaetxe, I.; Johnson, P. H.; Muzzi, F.; Greenfield, M.; Durkan, M.; Leong, Y. S.; Dong, Y.; Cook, H.; Axford, J.; Callahan, A. G.; Kenny, N.; Omodei, C.; McGraw, E. A.; Ryan, P. A.; Ritchie, S. A.; Turelli, M.; O’Neill, S. L., Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission. Nature, 454-457 (2011) |
| [14] | Hu, L.; Huang, M.; Tang, M.; Yu, J.; Zheng, B., Wolbachia spread dynamics in stochastic environments. Theor. Popul. Biol., 32-44 (2015) · Zbl 1343.92482 |
| [15] | Hu, L.; Huang, M.; Tang, M.; Yu, J.; Zheng, B., Wolbachia spread dynamics in multi-regimes of environmental conditions. J. Theor. Biol., 247-258 (2019) · Zbl 1406.92578 |
| [16] | Hu, L.; Tang, M.; Wu, Z.; Xi, Z.; Yu, J., The threshold infection level for Wolbachia invasion in random environments. J. Differ. Equ., 4377-4393 (2019) · Zbl 1406.34072 |
| [17] | Hu, L.; Yang, C.; Hui, Y.; Yu, J., Mosquito control based on pesticides and endosymbiotic bacterium Wolbachia. Bull. Math. Biol., 58 (2021) · Zbl 1466.92186 |
| [18] | Huang, M.; Luo, J.; Hu, L.; Zheng, B.; Yu, J., Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations. J. Theor. Biol., 1-11 (2018) · Zbl 1400.92490 |
| [19] | Ikeda, N.; Watanabe, S., Stochastic Differential Equations and Diffusion Processes (1989), North-Holland Publishing Company: North-Holland Publishing Company Amsterdam · Zbl 0684.60040 |
| [20] | Iturbe-Ormaetxe, I.; Walker, T.; O’Neill, S. L., Wolbachia and the biological control of mosquito-borne disease. EMBO Rep., 508-518 (2011) |
| [21] | Jansen, V. A.A.; Turelli, M.; Godfray, H. C.J., Stochastic spread of Wolbachia. Proc. R. Soc. Lond. B, Biol. Sci., 2769-2776 (2008) |
| [22] | Kallenberg, O., Foundations of Modern Probability (2002), Springer-Verlag: Springer-Verlag New York · Zbl 0996.60001 |
| [23] | Khasminskii, R., Stochastic Stability of Differential Equations (2012), Springer: Springer Heidelberg · Zbl 1259.60058 |
| [24] | Kyle, J. L.; Harris, E., Global spread and persistence of dengue. Annu. Rev. Microbiol., 71-92 (2008) |
| [25] | Li, X.; Gray, A.; Jiang, D.; Mao, X., Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. J. Math. Anal. Appl., 11-28 (2011) · Zbl 1205.92058 |
| [26] | Li, X.; Mao, X.; Yin, G., Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in \(p\) th moment and stability. IMA J. Numer. Anal., 847-892 (2019) · Zbl 1461.65007 |
| [27] | Li, X.; Song, G.; Xia, Y.; Yuan, C., Dynamical behaviors of the tumor-immune system in a stochastic environment. SIAM J. Appl. Math., 2193-2217 (2019) · Zbl 1439.92065 |
| [28] | Mao, X.; Yuan, C., Stochastic Differential Equations with Markovian Switching (2006), Imperial College Press: Imperial College Press London · Zbl 1126.60002 |
| [29] | Nguyena, D. H.; Yin, G.; Zhu, C., Certain properties related to well posedness of switching diffusions. Stoch. Process. Appl., 3135-3158 (2017) · Zbl 1372.60117 |
| [30] | Ong, S., Wolbachia goes to work in the war on mosquitoes. Nature (2021), S32-S34 |
| [31] | Otero, M.; Schweigmann, N.; Solari, H. G., A stochastic spatial dynamical model for Aedes aegypti. Bull. Math. Biol., 1297-1325 (2008) · Zbl 1142.92028 |
| [32] | Predescu, M.; Sirbu, G.; Levins, R.; Awerbuch-Friedlander, T., On the dynamics of a deterministic and stochastic model for mosquito control. Appl. Math. Lett., 919-925 (2007) · Zbl 1128.92041 |
| [33] | Qu, Z.; Xue, L.; Hyman, J. M., Modeling the transmission of Wolbachia in mosquitoes for controlling mosquito-borne disease. SIAM J. Appl. Math., 826-852 (2018) · Zbl 1392.92107 |
| [34] | Rasić, G.; Endersby, N. M.; Williams, C.; Hoffmann, A. A., Using Wolbachia-based release for suppression of Aedes mosquitoes: insights from genetic data and population simulations. Ecol. Appl., Publ. Ecol. Soc. Am., 1226-1234 (2014) |
| [35] | Schreiber, S. J., Persistence for stochastic difference equations: a mini-review. J. Differ. Equ. Appl., 1381-1403 (2012) · Zbl 1258.39010 |
| [36] | Somwang, P.; Yanola, J.; Suwan, W.; Walton, C.; Lumjuan, N.; Prapanthadara, L.; Somboon, P., Enzymes-based resistant mechanism in pyrethroid resistant and susceptible Aedes aegypti strains from northern Thailand. Parasitol. Res., 531-537 (2011) |
| [37] | Tuong, T. D.; Nguyen, N. N.; Yin, G., Longtime behavior of a class of stochastic tumor-immune systems. Syst. Control Lett. (2020) · Zbl 1453.92083 |
| [38] | Turelli, M.; Hoffmann, A. A., Microbe-induced cytoplasmic incompatibility as a mechanism for introducing transgenes into arthropod populations. Insect Mol. Biol., 243-255 (1999) |
| [39] | Walker, T.; Johnson, P. H.; Moreira, L. A.; Iturbe-Ormaetxe, I.; Frentiu, F. D.; McMeniman, C. J.; Leong, Y. S.; Dong, Y.; Axford, J.; Kriesner, P.; Lloyd, A. L.; Ritchie, S. A.; O’Neill, S. L.; Hoffmann, A. A., The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature, 450-453 (2011) |
| [40] | Werren, J. H., Biology of Wolbachia. Annu. Rev. Entomol., 587-609 (1997) |
| [41] | Yang, H. M.; Macoris, M. L.G.; Galvani, K. C.; Andrighetti, M. T.M.; Wanderley, D. M.V., Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue. Epidemiol. Infect., 1188-1202 (2009) |
| [42] | Yu, J., Existence and stability of a unique and exact two periodic orbits for an interactive wild and sterile mosquito model. J. Differ. Equ., 10395-10415 (2020) · Zbl 1457.34084 |
| [43] | Yu, J.; Li, J., A mosquito population suppression model by releasing Wolbachia-Infected males. J. Biol. Dyn., 606-620 (2019) · Zbl 1448.92260 |
| [44] | Yu, J.; Li, J., Global asymptotic stability in an interactive wild and sterile mosquito model. J. Differ. Equ., 6193-6215 (2020) · Zbl 1444.34103 |
| [45] | Yu, J.; Li, J., A delay suppression model with sterile mosquitoes release period equal to wild larvae maturation period. J. Math. Biol., 14 (2022) · Zbl 1489.34120 |
| [46] | Zhang, X.; Liu, Q.; Zhu, H., Modeling and dynamics of Wolbachia-infected male releases and mating competition on mosquito control. J. Math. Biol., 243-276 (2020) · Zbl 1448.34106 |
| [47] | Zheng, B.; Li, J.; Yu, J., One discrete dynamical model on the Wolbachia infection frequency in mosquito populations. Sci. China Math., 1749-1764 (2022) · Zbl 1497.92333 |
| [48] | Zheng, B.; Li, J.; Yu, J., Existence and stability of periodic solutions in a mosquito population suppression model with time delay. J. Differ. Equ., 159-178 (2022) · Zbl 1492.34085 |
| [49] | Zheng, B.; Tang, M.; Yu, J., Modeling Wolbachia spread in mosquitoes through delay differential equation. SIAM J. Appl. Math., 743-770 (2014) · Zbl 1303.92124 |
| [50] | Zheng, B.; Yu, J.; Li, J., Modeling and analysis of the implementation of the Wolbachia incompatible and sterile insect technique for mosquito population suppression. SIAM J. Appl. Math., 718-740 (2021) · Zbl 1468.34074 |
| [51] | Zhu, C.; Yin, G., On strong feller, recurrence, and weak stabilization of regime-switching diffusions. SIAM J. Control Optim., 2003-2031 (2009) · Zbl 1282.93201 |
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