Qualitative analysis of peer influence effects on testing of infectious disease model. (English) Zbl 07827983
Sharma, Rajesh Kumar (ed.) et al., Frontiers in industrial and applied mathematics. Selected papers based on the presentations at the 4th international conference, FIAM-2021, Punjab, India, December 21–22, 2021. Singapore: Springer. Springer Proc. Math. Stat. 410, 201-213 (2023).
Summary: Outbreaks minimization has become the need of the hour. If we start clouding the list of infectious diseases, the list will point out that there is a rise in infectious diseases in the current era, and after the first case of any illness for knowing about its spread, testing methods are introduced. So testing plays a key role, and it is necessary to detect any infectious disease effects on humans. However, the peer influence effect of persons who have recovered from disease without visiting any doctor encourages other people to not get tested and take self-medication. They do not understand the need for tests and spread fake scenarios convincing others to follow them. The paper studies the impact of these individuals on the emergence of the disease by analyzing the mathematical model proposed in the situation, which is further analyzed and studied through simulation. The analysis section comprises local and global stability of the equilibrium points, primary reproduction number, and threshold analysis of the proposed model. Numerical simulation has provided a clear view of the qualitative analysis through the graphs and the plots.
For the entire collection see [Zbl 1524.76004].
For the entire collection see [Zbl 1524.76004].
MSC:
| 76-XX | Fluid mechanics |
Keywords:
peer-effect; testing; infectious disease; reproduction number; Lyapunov; Liénard chipart criterion; threshold analysisReferences:
| [1] | Bernoulli, D.: Essai d’une nouvelle analyse de la mortalite causee par la petite verole. Mem. Math. Phys. Acad. Roy. Sci., Paris (1766) |
| [2] | Biswas, S.K., Ghosh, J.K., Sarkar, S., Ghosh, U.: COVID-19 Pandemic in India: A Mathematical Model Study. Springer Nature B.V (2020). doi:10.1007/s11071-020-05958-z · Zbl 1517.92024 |
| [3] | Brauer, F., Chavez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, New York (2011). ISSN:978-1-4757-3516-1 |
| [4] | Buonomo, B.; Lacitignola, D., Modeling peer influence effects on the spread of high-risk alcohol consumption behavior, Ricerche mat., 63, 101-117 (2014) · Zbl 1330.92121 · doi:10.1007/s11587-013-0167-3 |
| [5] | Cani, J.; Yakowitz, S.; Blount, M., The spread and quarantine of HIV infection in a prison system, Soc. Ind. Appl. Math. J. Appl. Math., 57, 1510-1530 (1997) · Zbl 0892.92021 · doi:10.1137/S0036139995283237 |
| [6] | Daud, A.A.M.: A note on Lienard-Chipart criteria and its application to epidemic models. Math. Stat. 9, 41-45 (2021). doi:10.13189/ms.2021.090107 |
| [7] | Dhar, J.; Sharma, A., The role of the incubation period in a disease model, Appl. Math. e-Notes, 9, 146-153 (2009) · Zbl 1163.92024 |
| [8] | Erdem, M.; Safan, M.; Chavez, C., Mathematical analysis of an SIQR influenza model with imperfect quarantine, Bull. Math. Biol., 79, 1612-1636 (2017) · Zbl 1372.92103 · doi:10.1007/s11538-017-0301-6 |
| [9] | Esteva, L.; Gumel, AB; Vargas, C., Qualitative study of transmission dynamics of drug-resistant malaria, Math. Comput. Model., 50, 611-630 (2009) · Zbl 1185.34061 · doi:10.1016/j.mcm.2009.02.012 |
| [10] | Esteva, L.; Vargas, C., Influence of vertical and mechanical transmission on the dynamics of dengue disease, Math. Biosci., 167, 51-64 (2000) · Zbl 0970.92011 · doi:10.1016/s0025-5564(00)00024-9 |
| [11] | Hale, J.K.: Ordinary Differential Equations. Wiley, New York (1969) · Zbl 0186.40901 |
| [12] | Hamer, WH, The Milroy lectures on epidemic disease in England-the evidence of variability and persistence of type, The Lancet, 1, 733-739 (1906) |
| [13] | Hethcote, HW; Thieme, HR, Stability of the endemic equilibrium in epidemic models with subpopulations, Math. Biosci., 75, 205-227 (1985) · Zbl 0582.92024 · doi:10.1016/0025-5564(85)90038-0 |
| [14] | Hethcote, H.; Ma, Z.; Shengbing, L., Effects of quarantine in six endemic models for infectious diseases, Math. Biosci., 180, 141-160 (2002) · Zbl 1019.92030 · doi:10.1016/s0025-5564(02)00111-6 |
| [15] | Hethcote, HW; Ma, Z.; Liao, SB, Effects of quarantine in six endemic models for infectious diseases, Math. Biosci., 180, 141-160 (2002) · Zbl 1019.92030 · doi:10.1016/s0025-5564(02)00111-6 |
| [16] | Hyman, JM; Li, J., Modeling the effectiveness of isolation strategies in preventing STD epidemics, Soc. Ind. Appl. Math. J. Appl. Math., 58, 912-925 (1998) · Zbl 0905.92027 · doi:10.1137/S003613999630561X |
| [17] | Khan, MA; Atangana, A., Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative, Alex. Eng. J., 59, 2379-2389 (2020) · doi:10.1016/j.aej.2020.02.033 |
| [18] | Lakshmikantham, V., Leela, M.S., Matynyuk, A.A.: Stability Analysis of Nonlinear Systems. Marcel Dekker Incorporated New York and Basel (1989) · Zbl 0676.34003 |
| [19] | La Salle, J.P.: The stability of dynamical systems. Soc. Ind. Appl. Math. (1976) |
| [20] | Lee, SH; Kang, H.; Song, HS, Effect of Individual self-protective behavior on epidemic spreading, J. Biol. Syst., 27, 531-542 (2019) · Zbl 1427.92088 · doi:10.1142/S0218339019500219 |
| [21] | Misra, A.K., Rai, R.K., Takeuchi, Y.: Modeling the effect of time delay in budget allocation to control an epidemic through awareness. Int. J. Biomath. 11 (2018). doi:10.1142/S1793524518500274 · Zbl 1387.34022 |
| [22] | Perko, L.: Differential Equations and Dynamical Systems. Springer, New York (1996). doi:10.1007/978-1-4684-0249-0 · Zbl 0854.34001 |
| [23] | Ross, R.: The Prevention of Malaria, 2nd edn. John Murray, London (1911) |
| [24] | Safi, MA; Gumelb, AB, Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals, J. Math. Anal. Appl., 399, 565-575 (2013) · Zbl 1259.34037 · doi:10.1016/j.jmaa.2012.10.015 |
| [25] | Sahu, GP; Dhar, J., Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Appl. Math. Model., 36, 908-923 (2012) · Zbl 1243.34068 · doi:10.1016/j.apm.2011.07.044 |
| [26] | Sahua, GP; Dhar, J., Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity, J. Math. Anal. Appl., 421, 1651-1672 (2015) · Zbl 1365.92131 · doi:10.1016/j.jmaa.2014.08.019 |
| [27] | Ullah, S., Khan, M.A.: Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study. Chaos, Solitons Fractals 139 (2020). doi:10.1016/j.chaos.2020.110075 |
| [28] | Van den Driesschea, P.; Wamough, J., Reproduction number and sub-threshold endemic equilibria for compartment models of disease transmisson, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6 |
| [29] | Wang, S.; Xu, F.; Rong, L., Bistability analysis of an HIV model with immune response, Journal of Biological System, 25, 677-695 (2017) · Zbl 1397.92410 · doi:10.1142/S021833901740006X |
| [30] | WHO. https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200311-sitrep-51-covid-19.pdf?sfvrsn=1ba62e57-10 |
| [31] | WHO. https://covid19.who.int/ |
| [32] | Xing, Z.; Cardona, CJ, Pre-existing immunity to pandemic (H1N1) 2009, Emerg. Infect. Dis., 15, 1847-1849 (2009) · doi:10.3201/eid1511.090685 |
| [33] | Zhou, X.; Cui, J., Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate, Nonlinear Dyn., 63, 639-653 (2011) · doi:10.1007/S11071-010-9826-Z |
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.
