Time-varying sensitivity analysis of an influenza model with interventions. (English) Zbl 1492.92105
Summary: We formulate an influenza model with treatment and vaccination. Both time invariant and time-dependent uncertainty analyses and sensitivity analysis of the model parameter values are carried out to understand the dependence of the reproduction numbers and model state variables on their components. Results show that the relationship between treatment and epidemic size is nonlinear and that there exists a critical threshold treatment rate under which treatment is beneficial. Sensitivity analysis suggests that the most significant parameters are those related to infection transmission, infectiousness, duration of infectiousness and waning immunity. Further, there are important instances when the relationship between some parameters and model outputs changes behavior from negatively to positively correlated or vice versa because all sensitivity indices, except \(\beta_S\) are functions of other parameters and thus will change with the change in parameter values. For example, treatment helps to lower the epidemic size, but may then become a “source” of infection likely due to resistance de novo. This knowledge is critical for proper public health planning and guidance of control strategies.
Keywords:
influenza model; biomedical interventions; basic reproductive number; sensitivity and uncertainty analyses; Latin hypercube sampling; partial rank correlation coefficientReferences:
| [1] | Njeuhmeli, E., Schnure, M., Vazzano, A., Gold, E., Stegman, P., Kripke, K., Tchuenche, M., Bollinger, L., Forsythe, S. and Hankins, C., Using mathematical modeling to inform health policy: A case study from voluntary medical male circumcision scale-up in eastern and southern Africa and proposed framework for success, PLOS One14 (2019) e0213605. |
| [2] | Gilbert, J. A., Meyers, L. A., Galvani, A. P. and Townsend, J. P., Probabilistic uncertainty analysis of epidemiological modeling to guide public health intervention policy, Epidemics6 (2014) 37-45. |
| [3] | Rwezaura, H., Mtisi, E. and Tchuenche, J. M., A mathematical analysis of influenza with treatment and vaccination, in Infectious Disease Modelling Research Progress, , eds. Tchuenche, J. M. and Chiyaka, C. (Nova Science Publishers, Hauppauge, NY, 2010), pp. 31-84. · Zbl 1181.92058 |
| [4] | Marino, S., Hogue, I. B., Ray, C. J. and Kirschner, D. E., A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theoret. Biol.254 (2008) 178-196. · Zbl 1400.92013 |
| [5] | Arriola, L. and Hyman, J. M., Sensitivity analysis for uncertainty quantification in mathematical models, in Mathematical and Statistical Estimation Approaches in Epidemiology (Springer, Dordrecht, 2009), pp. 195-247. · Zbl 1345.92001 |
| [6] | van den Driessche, P. and Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci.180 (2002) 29-48. · Zbl 1015.92036 |
| [7] | Keeling, M. J. and Rohani, P., Modeling Infectious Diseases in Humans and Animals (Princeton University Press, 2008). · Zbl 1279.92038 |
| [8] | Chitnis, N., Hyman, J. M. and Cushing, J. M., Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol.70 (2008) 1272-1296. · Zbl 1142.92025 |
| [9] | Massad, E., Behrens, R. H., Burattini, M. N. and Coutinho, F. A., Modeling the risk of malaria for travelers to areas with stable malaria transmission, Malaria J.8 (2009) 1-7. |
| [10] | Samsuzzoha, M., Singh, M. and Lucy, D., Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza, Appl. Math. Model.37 (2013) 903-915. · Zbl 1352.92168 |
| [11] | Blower, S. M. and Dowlatabadi, H., Sensitivity and uncertainty analysis of complex models of disease transmission: An HIV model, as an example, Int. Stat. Rev.62 (1994) 229-243. · Zbl 0825.62860 |
| [12] | Sanchez, M. A. and Blower, S. M., Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example, Am. J. Epidemiol.145 (1997) 1127-1137. |
| [13] | Pedro, S., Tonnang, H. and Abelman, S., Uncertainty and sensitivity analysis of a rift valley fever model, Appl. Math. Comput.279 (2016) 170-186. · Zbl 1410.92133 |
| [14] | Pedro, S., Rwezaura, H., Mandipezar, A. and Tchuenche, J. M., Qualitative analysis of an influenza model with biomedical interventions, Chaos Solitons Fractals146 (2021) 110852. |
| [15] | Lipsitch, M., Cohen, T., Murray, M. and Levin, B. R., Antiviral resistance and the control of pandemic influenza, PLOS Med.4 (2007) e15. |
| [16] | Mathews, J. D., McCaw, C. T., McVernon, J., McBryda, E. S. and McCaw, J. M., A biological model for influenza transmission: Pandemic planning implications of asymptomatic infection and immunity, PLOS One2 (2017) e1220. |
| [17] | Qiu, Z. and Feng, Z., Transmission dynamics of an influenza model with vaccination and antiviral treatment, Bull. Math. Biol.72 (2010) 1-33. · Zbl 1184.92032 |
| [18] | Foy, H. M., Cooney, M. K. and McMahan, R., A Hong Kong influenza immunity three years after immunization, JAMA226 (1973) 758-761. |
| [19] | Quan, F. S., Kim, Y. C., Song, J. M., Hwang, H. S., Compans, R. W., Prausnitz, M. R. and Kang, S. M., Long-term protective immunity from an influenza virus-like particle vaccine administered with a microneedle patch, Clin. Vaccine Immunol.20 (2013) 1433-1439. |
| [20] | Stilianakis, N. I., Perelson, A. S. and Hayden, F. G., Emergence of drug resistance during an influenza epidemic: Insights from a mathematical model, J. Infect. Dis.177 (1998) 863-873. |
| [21] | Chao, D. L., Bloom, J. D., Kochin, B. F., Antia, R. and Longini, I. M., The global spread of drug-resistant influenza, J. R. Soc. Interface9 (2012) 648-656. |
| [22] | Diekmann, O., Heesterbeek, J. A. and Metz, J. A., On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol.28 (1990) 365-382. · Zbl 0726.92018 |
| [23] | Andreasen, V., The final size of an epidemic and its relation to the basic reproduction number, Bull. Math. Biol.73 (2011) 2305-2321. · Zbl 1334.92388 |
| [24] | Koella, J. C. and Antia, R., Epidemiological models for the spread of anti-malarial resistance, Malaria J.2 (2003) 3. |
| [25] | Biggerstaff, M., Cauchemez, S., Reed, C., Gambhir, M. and Finelli, L., Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: A systematic review of the literature, BMC Infect. Dis.14 (2014) 480. |
| [26] | Fiore, A. E., Uyeki, T. M., Broder, K., Finelli, L., Euler, G. L., Singleton, J. A., Iskander, J. K., Wortley, P. M., Shay, D. K., Bresee, J. S. and Cox, N. J., Prevention and control of influenza with vaccines: Recommendations of the Advisory Committee on Immunization Practices (ACIP), MMWR59 (2010) 1-62. |
| [27] | Monto, A. S., Gravenstein, S., Elliott, M., Colopy, M. and Schweinle, J., Clinical signs and symptoms predicting influenza infection, Arch. Intern. Med.160 (2000) 3243-3247. |
| [28] | Ferguson, N. M., Cummings, D. A. T., Fraser, C., Cajka, J. C., Cooley, P. C. and Burke, D. S., Strategies for mitigating an influenza pandemic, Nature442 (2006) 448-452. |
| [29] | Gaff, H. D., Hartley, D. M. and Leahy, N. P., An epidemiological model of rift valley fever, Electron. J. Differ. Equ.2007 (2007) 1-12. · Zbl 1138.34324 |
| [30] | Niu, T., Gaff, H. D., Papelis, Y. E. and Hartley, D. M., An epidemiological model of rift valley fever with spatial dynamics, Comput. Math. Methods Med.2012 (2012) 138757. · Zbl 1401.92196 |
| [31] | Tchuenche, J. M., Khamis, S. A., Agusto, F. B. and Mpeshe, S. C., Optimal control and sensitivity analysis of an influenza model with treatment and vaccination, Acta Biotheor.59 (2011) 1-28. |
| [32] | Mills, C. E., Robins, J. M. and Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature432 (2004) 904-946. |
| [33] | Xiao, H. and Duan, Y., Sensitivity analysis of correlated inputs: Application to a riveting process model, Appl. Math. Mod.40 (2016) 6622-6638. · Zbl 1465.62130 |
| [34] | B. Gomero, Latin hypercube sampling and partial rank correlation coefficient analysis applied to an optimal control problem, Master’s Thesis, University of Tennessee (2012), https://trace.tennessee.edu/utk_gradthes/1278. |
| [35] | Nsoesie, E. O., Beckman, R. J. and Marathe, M. V., Sensitivity analysis of an individual-based model for simulation of influenza epidemics, PLOS One7 (2012) e45414. |
| [36] | Taghizadeh, L., Karimi, K. and Heitzinger, C., Uncertainty quantification in epidemiological models for the COVID-19 pandemic, Comput. Biol. Med.125 (2020) 104011. |
| [37] | Seaholm, S. K., Ackerman, E. and Wu, S. C., Latin hypercube sampling and the sensitivity analysis of a Monte Carlo epidemic model, Int. J. Biomed. Comput.23 (1988), 97-112. |
| [38] | Frey, H. C. and Patil, S. R., Identification and review of sensitivity analysis methods, Risk Anal.22 (2002) 553-578. |
| [39] | Hamby, D., A comparison of sensitivity analysis techniques, Health Phys.68(2) (1995) 195-204. |
| [40] | Cacuci, D. G., Ionescu-Bujor, M. and Navon, I. M., Sensitivity and Uncertainty Analysis, Volume II: Applications to Large-scale Systems, Vol. 2 (CRC Press, 2005). · Zbl 1083.60002 |
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.
