Predicting Dynamics of an Infectious Disease
Keywords:Infectious Disease, Epidemiology, SIR Model
In a broader sense, disease is either infectious or not infectious. Such a classification purely rely weather a disease can be passed or transmitted between individuals or not. Infectious diseases are those diseases that can spread or transmitted easily and influenza is an example. Non- infectious diseases seem to develop over an individualâ€™s lifespan and are not transmittable as such. Disease such as arthritis is an example of non-infectious disease. Classification of diseases is not an easy touch and in principle we have to admit to some overlapping situations. Some infectious diseases although not necessary for developing can be a cause for non-infectious disease such as cancer. There is however a clear distinction in carrying out epidemiological study for each disease type. The epidemiologic interest in studying non-infectious disease lies primarily on identifying the risk factors that are prominent in the chance of developing a particular disease. This could for example be learning the risk of contracting lung cancer attributed to smoking. In studying infectious disease on contrary, the epidemiologic interest would be identifying the infectious cause, origin and pattern of the disease in a population of interest. A study of disease outbreak in a local population where the primary risk factor for catching an infectious disease is the presence of an outbreak itself is example in this case . This paper focuses on learning the great predictive power of models for infectious disease at population scale over the short period of time. The paper is a build-up on the same idea to examine infectious disease transmission mechanisms from host to another caused by micro parasitic pathogens. The paper does not cover cases where a disease is transmitted by macro parasite intermediate vectors enter the dynamic of the model. The examination of the model is based on constant and susceptible healthy, infected and immune population without no vital (birth and death) statistics.
. Bailey Ntj. The mathematical theory of infectious diseases. London: Griffin, 1975.
. Anderson RM, May RM. Infectious diseases of humans. Oxford: Oxford University Press, 1991.
. Black FL Measles. In: Evans AS ed. viral infections of humans: epidemiology and control. New York: Plenum Medical, 1984: 397.
. World Health Organization. Epidemiological and vital statistics report. 1952; 5: 332.
. Chapin CV. Measles in Providence, R.I. American Journal of Hygiene 1925; 5: 635-55.
. Evans AS. Epidemiological concepts and methods. In: Evans AS ed. viral infections of humans: epidemiology and control. New York: Plenum Medical, 1984: 20.
. Hamer. WH Epidemic diseases in England. Lancet 1906; i: 733-39.
. Soper. HE Interpretation of periodicity in disease prevalence. Journal of the Royal Statistical Society A 1929; 92: 34-73.
. Greenwood M. On the statistical measure of infectiousness. Journal of Hygiene 1931-31: 336-51.
. Cliff AD, Murray GD. A stochastic model for measles epidemics in a multi-region setting. Institute of British Geographers, Transactions New Series 1977; 2: 158-74.
. Fox JP. Herd immunity and measles. Reviews of Infectious Diseases 1983; 5: 463-66.
. Bailey Njt. The elements of stochastic processes. New York: Wiley, 1964: 183.
. Bartlett MS. Deterministic and stochastic models for recurrent epidemics. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and probability, 1956; 4:81-108.
. Nelder JA, Wedderburn Rwm. Generalised linear models. Journal of the Royal Statistical Society, 1972; 135: 370-84.
. Semple AB. Epidemiology of the influenza epidemic in Liverpool in 1950-51.Proceedings of the Royal Society of Medicine 1951; 44: 794-96.
. Kilbourne ED. The molecular epidemiology of influenza. Journal of Infectious Diseases1973; 127: 478-87.
. Fox JP, et al. Herd immunity: basic concept and relevance to public health immunization practices. American Journal of Epidemiology 1971; 94: 179-89.
. Elveback LR, et al. An influenza simulation model for immunization studies. American Journal of Epidemiology 1976; 103: 152-65.
. Longini I., et al. An optimization model for influenza A epidemics. Mathematical Biosciences 1978; 38: 141-57.
. Spicer CC. Mathematical modelling of influenza epidemics. British Medical Bulletin1979; 35: 23-28.
. Rvachev LA, Longini IM. A mathematical model for the global spread of influenza. Mathematical Biosciences 1985; 75: 3-22.
. Ross. R (1911). The Prevention of Malaria. London: John Murray. 651â€686p.
. Lyle D. Broemeling (2014). Bayesian Methods in Epidemiology. Taylor & Francis Group, LLC.
. Alan D. Lopez, et al. (2006). Global Burden of Disease and Risk Factors. The International Bank for Reconstruction and Development / The World Bank
. Fred Brauer, et al. (2008). Mathematical Epidemiology, Springer.
. Nicolas BacaÃ«r (2011). A Short History of Population Dynamics, Springer-Verlag London Limited.
. Herbert W. Hethcote (1978). An immunization model for a Heterogeneous Population, Academic press, Vol. 14, No 3, p338 â€“ 349.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.