Dynamical analysis of an age-structured dengue model with asymptomatic infection. (English) Zbl 1512.92109
This paper presents dynamics analysis of an age-structured dengue model with asymptomatic infection. The authors derive the basic reproduction number and obtain the global stability of the disease-free steady state. Moreover, they investigate the existence of the endemic steady states, backward bifurcation and uniform persistence.
Reviewer: Hongying Shu (Xi’an)
MSC:
| 92D30 | Epidemiology |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
References:
| [1] | Aguiar, M.; Ballesteros, S.; Kooi, B. W.; Stollenwerk, N., The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis, J. Theor. Biol., 289, 181-196 (2011) · Zbl 1397.92613 |
| [2] | Aguiar, M.; Anam, V.; Blyuss, K. B.; Estadilla, C. D.S.; Guerrero, B. V.; Knopoff, D., Mathematical models for dengue fever epidemiology: a 10-year systematic review, Phys. Life Rev., 40, 65-92 (2022) |
| [3] | Bhatt, S.; Gething, P. W.; Brady, O. J., The global distribution and burden of dengue, Nature, 496, 7446, 504-507 (2013) |
| [4] | Busenberg, S. N.; Iannelli, M.; Thieme, H. R., Global behavior of an age-structured epidemic model, SIAM J. Math. Anal., 22, 4, 1065-1080 (1991) · Zbl 0741.92015 |
| [5] | Cai, L. M.; Li, X. Z.; Song, X. Y., Permanence and stability of an age-structured prey-predator system with delays, Discrete Dyn. Nat. Soc., 2007, 149-174 (2007) |
| [6] | Cai, L. M.; Li, Z. Q.; Yang, C. Y.; Wang, J., Global analysis of an environmental disease transmission model linking within-host and between-host dynamics, Appl. Math. Model., 86, 404-423 (2020) · Zbl 1481.92133 |
| [7] | Cai, L. M.; Tuncer, N.; Martcheva, M., How does within-host dynamics affect population-level dynamics? Insights from an immuno-epidemiological model of malaria, Math. Methods Appl. Sci., 40, 18, 6424-6450 (2017) · Zbl 1383.92078 |
| [8] | Chong, G. F.; Cai, L. M., Analysis for an age-structured SVIR epidemic model with vaccination, (Proceedings of the 31st Chinese Control Conference (2012), IEEE), 1296-1300 |
| [9] | Cruz-Pacheco, G.; Esteva, L.; Vargas, C., Vaccination strategies for SIR vector-transmitted diseases, Bull. Math. Biol., 76, 8, 2073-2090 (2014) · Zbl 1300.92050 |
| [10] | Ding, C.; Wang, Z.; Zhang, Q., Age-structure model for oncolytic virotherapy, Int. J. Biomath., 15, 01, Article 2150091 pp. (2022) |
| [11] | Esteva, L.; Vargas, C., Coexistence of different serotypes of dengue virus, J. Math. Biol., 46, 31-47 (2003) · Zbl 1015.92023 |
| [12] | Farkas, J. Z.; Gourley, S. A.; Liu, R., Dengue transmission dynamics in age-structured human populations in the presence of Wolbachia (November 2021), available at |
| [13] | Ferguson, N.; Anderson, R.; Gupta, S., The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens, Proc. Natl. Acad. Sci., 96, 2, 790-794 (1999) |
| [14] | Hale, J. K., Asymptotic Behavior of Dissipative Systems (1988), AMS: AMS Providence · Zbl 0642.58013 |
| [15] | Harris, E.; Videa, E.; Pérez, L., Clinical, epidemiologic, and virologic features of dengue in the 1998 epidemic in Nicaragua, Am. J. Trop. Med. Hyg., 63, 1-2, 5-11 (2000) |
| [16] | He, C. Q.; Zhao, Y., Stability analysis of a dengue thermokinetic model with latent effects, Adv. Appl. Math., 10, 7, 2472-2485 (2021) |
| [17] | Hirsch, W. M.; Hanisch, H.; Gabriel, J.-P., Differential equation models of some parasitic infections: methods for the study of asymptotic behavior, Commun. Pure Appl. Math., 38, 6, 733-753 (1985) · Zbl 0637.92008 |
| [18] | Jan, R.; Khan, M. A.; GÓmez-Aguilar, J. F., Asymptomatic carriers in transmission dynamics of dengue with control interventions, Optim. Control Appl. Methods, 41, 2, 430-447 (2020) · Zbl 1467.92203 |
| [19] | Jan, R.; Xiao, Y., Effect of partial immunity on transmission dynamics of dengue disease with optimal control, Math. Methods Appl. Sci., 42, 6, 1967-1983 (2019) · Zbl 1418.34100 |
| [20] | Kabir, K. A.; Tanimoto, J., Cost-efficiency analysis of voluntary vaccination against n-serovar diseases using antibody-dependent enhancement: a game approach, J. Theor. Biol., 503, Article 110379 pp. (2020) · Zbl 1453.92190 |
| [21] | Li, X. Z.; Gupur, G., Global stability of an age-structured SIRS epidemic model with vaccination, Discrete Contin. Dyn. Syst., Ser. B, 4, 3, 643-652 (2004) · Zbl 1101.92042 |
| [22] | Maier, S. B.; Massad, E.; Amaku, M., The optimal age of vaccination against dengue with an age-dependent biting rate with application to Brazil, Bull. Math. Biol., 82, 1, 1-32 (2020) · Zbl 1432.92055 |
| [23] | Martcheva, M.; Thieme, H. R., Progression age enhanced backward bifurcation in an epidemic model with super-infection, J. Math. Biol., 46, 5, 385-424 (2003) · Zbl 1097.92046 |
| [24] | Mishra, A.; Gakkhar, S., Modeling of dengue with impact of asymptomatic infection and ADE factor, Differ. Equ. Dyn. Syst., 28, 3, 745-761 (2020) · Zbl 1447.92457 |
| [25] | Okuwa, K.; Inaba, H.; Kuniya, T., Mathematical analysis for an age-structured SIRS epidemic model, Math. Biosci. Eng., 16, 5, 6071-6102 (2019) · Zbl 1497.92291 |
| [26] | Pongsumpun, P.; Samana, D., Mathematical model for asymptomatic and symptomatic infections of dengue disease, WSEAS Trans. Biol. Biomed., 3, 3, 49-54 (2006) |
| [27] | Pongsumpun, P.; Tang, I. M., Transmission of dengue hemorrhagic fever in an age structured population, Math. Comput. Model., 37, 949-961 (2003) · Zbl 1045.92040 |
| [28] | Ranjit, S.; Kissoon, N., Dengue hemorrhagic fever and shock syndromes, Ped. Crit. Care Med., 12, 1, 90-100 (2011) |
| [29] | Rashkov, P.; Kooi, B. W., Complexity of host-vector dynamics in a two-strain dengue model, J. Biol. Dyn., 15, 1, 35-72 (2021) · Zbl 1490.92114 |
| [30] | Rocha, F.; Mateus, L.; Skwara, U.; Aguiar, M.; Stollenwerk, N., Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models, Int. J. Comput. Math., 93, 8, 1405-1422 (2016) · Zbl 1341.92077 |
| [31] | Sanchez, F.; Calvo, J. G., Dengue model with early-life stage of vectors and age-structure within host, Rev. Mat. Teor. Apl., 27, 1, 157-177 (2020) · Zbl 1513.93043 |
| [32] | Sanchez, F.; Calvo, J. G.; Segura, E., A partial differential equation model with age-structure and nonlinear recidivism: conditions for a backward bifurcation and a general numerical implementation, Comput. Math. Appl., 78, 12, 3916-3930 (2019) · Zbl 1443.92182 |
| [33] | Simmons, C. P.; Farrar, J. J.; van Vinh Chau, N.; Wills, B., Dengue, N. Engl. J. Med., 366, 15, 1423-1432 (2012) |
| [34] | Thieme, H. R., Uniform persistence and permanence for non-autonomous semiflows in population biology, Math. Biosci., 166, 2, 173-201 (2000) · Zbl 0970.37061 |
| [35] | Tian, X.; Wang, W. D., Dynamical analysis of age-structured pertussis model with covert infection, Math. Methods Appl. Sci., 43, 4, 1631-1645 (2020) · Zbl 1452.92042 |
| [36] | World Health Organization, Dengue and severe dengue, available at |
| [37] | Xie, Z.; Liu, X., Global dynamics in an age-structured HIV model with humoral immunity, Int. J. Biomath., 14, 06, Article 2150047 pp. (2021) · Zbl 1475.92057 |
| [38] | Yang, J. Y.; Mondnak, C.; Wang, J., Dynamical analysis and optimal control simulation for an age-structured cholera transmission model, J. Franklin Inst., 356, 15, 8438-8467 (2019) · Zbl 1423.92243 |
| [39] | Yosida, K., Functional Analysis (1968), Spring-Verlag · Zbl 0152.32102 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
