Mathematical Modeling of the Dynamics Transmission of Infectious Disease

Abstract

This thesis is designed for the study of the transmission of amoebiasis which is aligned newlinewith the theory of mathematical modeling of infectious diseases. The emphasis is put newline newlineon the development of mathematical models that allow the understanding of the dy- newlinenamics transmission of amoebiasis. Theoretical and numerical analysis of these models newline newlineyield results that help to discern the pattern and the configuration of the dynamics newlinespread of amoebiasis through the population. As far the derivation of the models as newlineconcern, we should notice that they are essentially built on the biological description newlineof Entamoeba Histolytica s cycle. Thus, literature available from a good number of newline newlineresearchers, who have written on amoebiasis and Entamoeba histolytica, plays an im- newlineportant role in the process of derivation of the models. The models derived follow newline newlinethe pattern drawn by the profile of amoebiasis as it is described through the cycle of newlineEntamoeba histolytica. newline newlineAccording to the literature and review of amoebiasis, the disease classifies uniquely an newlineindividual of the population in one and only one of the following five sub-populations newlinethat correspond to every stage of the development of amoebiasis. These subdivisions newline newlineare mainly: Susceptible, Exposed, Acute infectious, Carrier, Recovered. Their respec- newlinetive sizes are denoted by S, E, I, C and R. Under this point of view, the epidemic newline newlinemodels conected with amoebiasis spread should follow the model topology (SEICRS). newlineBasing our modeling procedures on how the cysts are produced within the biological newline newlinecycle process of Entamoeba histolytica, it is genuinely to suggest two main mathemat- newlineical models that the dynamics of the ameobiasis spread may follow. These models are newline newlineeither simultaneous infection stages taking place or carrier forward infectious stages newline newlinetaking place. For indirect contact, when the infectious environment V must be incor- newlineporated toward model prototype SV EICRS. newline newlineIn case of mathematical models for the direct spread (person-to-person) of amoebi- newlineasis, the transmission of infection is made effective via bilinear incidence terms, while newline newlinePage: x newline newlinein case of indirect, where the environment has major impact, the infection transmis- newlinesion follows the saturation incidence. In both models, the transfer of people between newline newlinedifferent epidemic sub-populations is regulated by the principle of mass-action. Thus, newlinethe course of amoebiasis will be manifestly characterized by instantaneous rates of newline newlinechange in sizes, with respect to the time, of the following five sub-population or epi- newlinedemiological classes: susceptible S, exposed E, infective I, carrier C and recovered newline newlineR. We denote that the models derived are novel. They result from the modification newlineof existing basic topological model SEIR deeply studied in mathematical modeling of newlineinfectious diseases.The