scholarly journals Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Deccy Y. Trejos ◽  
Jose C. Valverde ◽  
Ezio Venturino
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Discrete Time ◽  
Continuous Time ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Simulation Techniques ◽  
Biological Aspects ◽  
Tools And Methods

Abstract In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and methods needed to qualitatively analyze deterministic continuous-time models, formulated by ordinary differential equations, are also introduced, while its discrete-time counterparts are properly referenced. In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. Finally, we present some control strategies usually considered to prevent epidemic outbreaks and their implementation in the model.

scholarly journals Modeling the spread of porcine reproductive and respiratory syndrome virus (PRRSV) in a swine population: transmission dynamics, immunity information, and optimal control strategies

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Phithakdet Phoo-ngurn ◽  
Chanakarn Kiataramkul ◽  
Farida Chamchod
Keyword(s):  
Mathematical Model ◽  
Vaccination Coverage ◽  
Control Strategies ◽  
Vaccination Rate ◽  
Transmission Dynamics ◽  
Respiratory Syndrome Virus ◽  
Respiratory Problems ◽  
Prrs Virus ◽  
Swine Population ◽  
Swine Disease

Abstract Porcine reproductive and respiratory syndrome (PRRS) is an important swine disease that affects many swine industries worldwide. The disease can cause reproductive failure and respiratory problems in a swine population. As vaccination is an important tool to control the spread of PRRS virus (PRRSV), we employ a mathematical model to investigate the transmission dynamics of PRRSV and the effects of immunity information, as well as vaccination control strategies. We also explore optimal vaccination coverage and vaccination rate to minimize the number of infected swines and vaccination efforts. Our results suggest that: (i) higher vaccination coverage and vaccination rate together with prior knowledge about immunity may help reduce the prevalence of PRRSV, and (ii) longer maximum vaccination efforts are required when swines stay longer in a population and it takes them longer time to recover from PRRS infections.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

scholarly journals Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

2020 ◽  
Author(s):  
Ibrahim M. ELmojtaba ◽  
Fatma Al-Musalhi ◽  
Asma Al-Ghassani ◽  
Nasser Al-Salti
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Environmental Transmission ◽  
Estimated Parameters ◽  
Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

scholarly journals Refutation of a Rumor by the Mass Media: Mathematical Model and Numerical Experiments

2021 ◽  
Vol 24 (2) ◽  
pp. 371-386
Author(s):  
Александр Петрович Михайлов ◽  
Александр Пхоун Чжо Петров
Keyword(s):  
Mathematical Model ◽  
Mass Media ◽  
Discrete Time ◽  
Continuous Time ◽  
Numerical Experiments ◽  
Mathematical Properties ◽  
The Media ◽  
The Mass Media

The process is considered, in which an unreliable rumor spreads in society, which is opposed by the broadcasting of the mass media. In this case, the unreliability of hearing is understood so that the information of the media contains a refutation and thereby inoculates individuals, that is, makes them immune to hearing. At the same time, individuals who have managed to accept the rumor cease to trust the media and thereby become unavailable for persuasion. For this process, a mathematical model is proposed in two versions. The variant with continuous time reveals some of the mathematical properties of the model. The discrete time option is more convenient for analyzing real processes since it allows one to estimate the parameters of the model. To assess these parameters, data on the ratings of the main socio-political programs of Russian TV channels were used. Several scenario calculations of the model with these parameters are presented. The main conclusion is that if the information disseminated by the media is not viral, that is, it is not retold by viewers to their neighbors in society, then the media are unable to resist rumors.

TRANSMISSION DYNAMICS AND CONTROL STRATEGIES OF COVID-19 IN WUHAN, CHINA

2020 ◽  
Vol 28 (03) ◽  
pp. 543-560 ◽  
Author(s):  
LIUYONG PANG ◽  
SANHONG LIU ◽  
XINAN ZHANG ◽  
TIANHAI TIAN ◽  
ZHONG ZHAO
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Public Awareness ◽  
Control Measures ◽  
Transmission Dynamics ◽  
Published Data ◽  
Model Parameters ◽  
Strict Control ◽  
Dynamics And Control ◽  
Numerical Calculation Method

In December 2019, a novel coronavirus, SARS-COV-2, was identified among patients in Wuhan, China. Two strict control measures, i.e., putting Wuhan on lockdown and taking strict quarantine rule, were carried out to contain the spread of COVID-19. Based on the different control measures, we divided the transmission process of COVID-19 into three stages. An SEIHR model was established to describe the transmission dynamics and was applied to fit the published data on the confirmed cases of Wuhan city from December 31, 2019 to March 25, 2020 to deduce the time when the first patient with COVID-19 appeared. The basic reproduction number was estimated in the first stage to demonstrate the number of secondary infectious cases generated by an average infectious case in the absence of policy intervention. The effective reproduction numbers in second and third stages were estimated to evaluate the effects of the two strict control measures. In addition, sensitivity analysis of the reproduction number according to model parameters was executed to demonstrate the effect of the control measures for containing the spread of COVID-19. Finally, the numerical calculation method was applied to investigate the influence of the different control measures on the spread of COVID-19. The results indicated that following the strict quarantine rule was very effective, and reducing the effective contact rates and improving the diagnosis rate were crucial in reducing the effective reproduction number, and taking control measures as soon as possible can effectively contain a larger outbreak of COVID-19. But a bigger challenge for us to contain the spread of COVID-19 was the transmission from the asymptomatic carriers, which required to raising the public awareness of self-protection and keeping a good physical protection.

scholarly journals A Stochastic Model for Malaria Transmission Dynamics

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Rachel Waema Mbogo ◽  
Livingstone S. Luboobi ◽  
John W. Odhiambo
Keyword(s):  
Infectious Diseases ◽  
Stochastic Model ◽  
Malaria Transmission ◽  
Stochastic Models ◽  
Continuous Time ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infected Mosquito ◽  
Deterministic Models ◽  
Discrete State

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

scholarly journals Dynamics of swine influenza model with optimal control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Takasar Hussain ◽  
Muhammad Ozair ◽  
Kazeem Oare Okosun ◽  
Muhammad Ishfaq ◽  
Aziz Ullah Awan ◽  
...  
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Swine Influenza ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
And Control ◽  
Disease Free ◽  
Good Agreement

AbstractTransmission dynamics of swine influenza pandemic is analysed through a deterministic model. Qualitative analysis of the model includes global asymptotic stability of disease-free and endemic equilibria under a certain condition based on the reproduction number. Sensitivity analysis to ponder the effect of model parameters on the reproduction number is performed and control strategies are designed. It is also verified that the obtained numerical results are in good agreement with the analytical ones.

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