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Li K, Wang J, Xie J, Rui J, Abudunaibi B, Wei H, Liu H, Zhang S, Li Q, Niu Y, Chen T. Advancements in Defining and Estimating the Reproduction Number in Infectious Disease Epidemiology. China CDC Wkly 2023; 5:829-834. [PMID: 37814634 PMCID: PMC10560332 DOI: 10.46234/ccdcw2023.158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/11/2023] [Indexed: 10/11/2023] Open
Affiliation(s)
- Kangguo Li
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayi Wang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayuan Xie
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jia Rui
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Buasiyamu Abudunaibi
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hongjie Wei
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hong Liu
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Shuo Zhang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Qun Li
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Yan Niu
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Tianmu Chen
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
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Kabir K, Ullah MS. Coupled simultaneous analysis of vaccine and self-awareness strategies on evolutionary dilemma aspect with various immunity. Heliyon 2023; 9:e14355. [PMID: 36950619 PMCID: PMC10025118 DOI: 10.1016/j.heliyon.2023.e14355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Revised: 03/01/2023] [Accepted: 03/02/2023] [Indexed: 03/12/2023] Open
Abstract
On evolutionary game theory (EGT), two intervention policies: vaccination and self-awareness, are considered to account for how human attitude impacts disease spreading. Although these interventions can impose, their implementation may depend on the various immunity systems such as shield immunity, innate immunity, waning immunity, natural immunity, and artificial immunity. This framework provides an epidemic SEIRVA (susceptible-exposed-infected-removed-vaccinated-aware) model and two EGT dynamics to analyze the interplay between the immunity system and social learning interventions. The prospect of exploring the individual's strategy and social dilemma for removing a disease could assist design an effective vaccine program and self-awareness policy. Also, we evaluated the indicator of social efficiency deficit (SED) for a social dual-dilemma to measure the presence of a dilemma situation. Extensive theoretical analysis displays that stability includes the reproduction number, conditions for positivity and uniqueness, and the strength number analyzed in the equilibria, including fundamental properties validated by numerical simulation of the discretization method that appraises a variety of graphs at adjusting parameters. We present extensive numerical studies investigating the affect of controlling parameters, individual vulnerability, optimal policies, and individual costs. It turns out that, even with the affordable vaccine, individuals may have very different behaviors; self-awareness strategy plays a vital role in controlling diseases.
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Affiliation(s)
- K.M.Ariful Kabir
- Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh
- Corresponding author.;
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Tomovski I, Basnarkov L, Abazi A. Endemic state equivalence between non-Markovian SEIS and Markovian SIS model in complex networks. PHYSICA A 2022; 599:127480. [PMID: 35529899 PMCID: PMC9055791 DOI: 10.1016/j.physa.2022.127480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/13/2022] [Revised: 04/21/2022] [Indexed: 06/14/2023]
Abstract
In the light of several major epidemic events that emerged in the past two decades, and emphasized by the COVID-19 pandemics, the non-Markovian spreading models occurring on complex networks gained significant attention from the scientific community. Following this interest, in this article, we explore the relations that exist between the mean-field approximated non-Markovian SEIS (Susceptible-Exposed-Infectious-Susceptible) and the classical Markovian SIS, as basic reoccurring virus spreading models in complex networks. We investigate the similarities and seek for equivalences both for the discrete-time and the continuous-time forms. First, we formally introduce the continuous-time non-Markovian SEIS model, and derive the epidemic threshold in a strict mathematical procedure. Then we present the main result of the paper that, providing certain relations between process parameters hold, the stationary-state solutions of the status probabilities in the non-Markovian SEIS may be found from the stationary state probabilities of the Markovian SIS model. This result has a two-fold significance. First, it simplifies the computational complexity of the non-Markovian model in practical applications, where only the stationary distributions of the state probabilities are required. Next, it defines the epidemic threshold of the non-Markovian SEIS model, without the necessity of a thrall mathematical analysis. We present this result both in analytical form, and confirm the result through numerical simulations. Furthermore, as of secondary importance, in an analytical procedure we show that each Markovian SIS may be represented as non-Markovian SEIS model.
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Affiliation(s)
- Igor Tomovski
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
| | - Lasko Basnarkov
- Faculty of Computer Science and Engineering, "Ss Cyril and Methodius" University - Skopje, ul.Rudzer Boshkovikj 16, P.O. Box 393, 1000 Skopje, Macedonia
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
| | - Alajdin Abazi
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428, 1000 Skopje, Macedonia
- South East European University, Ilindenska n.335, 1200 Tetovo, Macedonia
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Jones RP, Ponomarenko A. System Complexity in Influenza Infection and Vaccination: Effects upon Excess Winter Mortality. Infect Dis Rep 2022; 14:287-309. [PMID: 35645214 PMCID: PMC9149983 DOI: 10.3390/idr14030035] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/25/2022] [Revised: 04/12/2022] [Accepted: 04/18/2022] [Indexed: 02/01/2023] Open
Abstract
Unexpected outcomes are usually associated with interventions in complex systems. Excess winter mortality (EWM) is a measure of the net effect of all competing forces operating each winter, including influenza(s) and non-influenza pathogens. In this study over 2400 data points from 97 countries are used to look at the net effect of influenza vaccination rates in the elderly aged 65+ against excess winter mortality (EWM) each year from the winter of 1980/81 through to 2019/20. The observed international net effect of influenza vaccination ranges from a 7.8% reduction in EWM estimated at 100% elderly vaccination for the winter of 1989/90 down to a 9.3% increase in EWM for the winter of 2018/19. The average was only a 0.3% reduction in EWM for a 100% vaccinated elderly population. Such outcomes do not contradict the known protective effect of influenza vaccination against influenza mortality per se—they merely indicate that multiple complex interactions lie behind the observed net effect against all-causes (including all pathogen causes) of winter mortality. This range from net benefit to net disbenefit is proposed to arise from system complexity which includes environmental conditions (weather, solar cycles), the antigenic distance between constantly emerging circulating influenza clades and the influenza vaccine makeup, vaccination timing, pathogen interference, and human immune diversity (including individual history of host-virus, host-antigen interactions and immunosenescence) all interacting to give the observed outcomes each year. We propose that a narrow focus on influenza vaccine effectiveness misses the far wider complexity of winter mortality. Influenza vaccines may need to be formulated in different ways, and perhaps administered over a shorter timeframe to avoid the unanticipated adverse net outcomes seen in around 40% of years.
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Affiliation(s)
- Rodney P. Jones
- Healthcare Analysis & Forecasting, Wantage OX12 0NE, UK
- Correspondence:
| | - Andriy Ponomarenko
- Department of Biophysics, Informatics and Medical Instrumentation, Odessa National Medical University, Valikhovsky Lane 2, 65082 Odessa, Ukraine;
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Jain S, Kumar S. Dynamical analysis of SEIS model with nonlinear innate immunity and saturated treatment. EUROPEAN PHYSICAL JOURNAL PLUS 2021; 136:952. [PMID: 34549013 PMCID: PMC8447811 DOI: 10.1140/epjp/s13360-021-01944-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 09/02/2021] [Indexed: 05/06/2023]
Abstract
In this paper, we develop an SEIS model with Holling type II function representing the innate immunity as well as the saturated treatment. We obtain the existence and stability criteria for the equilibrium points. We observe that when the reproduction number is less than unity, the disease-free equilibrium always exists and is locally asymptotically stable. The multiple endemic equilibrium points can exist independent of the basic reproduction number, and the system may experience bistability. We find that the system can encounter backward or forward bifurcation at R 0 = 1 , where the contact rate β = β 0 is the bifurcation parameter. Therefore, the disease-free equilibrium may not be globally stable. We deduce the criteria for the presence of Hopf bifurcation where the parameter γ = γ ∗ acts as the bifurcation parameter and the system is a neutrally stable center. We also observe with the aid of a numerical example that a slight perturbation disrupts the neutral stability and the trajectories become either converging or diverging from the equilibrium point. Numerical simulation is performed with the help of MATLAB to justify the findings. We study the effect of nonlinearity of immunity function and the treatment rate on the dynamics of the disease spread. We find that when both are linear, the reproduction number is the same, but the system has a unique endemic equilibrium point that exists for reproduction number greater than unity. We find that there is neither backward bifurcation nor Hopf bifurcation. We also observe that the saturation in treatment enlarges the domain of backward bifurcation making disease eradication an extremely difficult task. The endemic equilibria in the case of saturated treatment may exist far more to the left of the bifurcation parameter β = β 0 . Hence, the nonlinearity of immunity function and treatment function affects the dynamics of an SEIS model highly; therefore, one must be precautious to choose an appropriate function for both while modeling.
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Affiliation(s)
- Shikha Jain
- Department of Mathematics, University of Delhi, Delhi, 110007 India
| | - Sachin Kumar
- Department of Mathematics, University of Delhi, Delhi, 110007 India
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