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Mathematical models of dengue transmission and control: A survey
Supriatna A.K.a, Nuraini N.b, Soewono E.b
a Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia
b Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]In this chapter we present mathematical models on dengue transmission and control. In the first part of the chapter we discuss a compartmental model for the transmissionof single strain virus of dengue via a set of ordinary differential equations. We showthe existence and the stability of the disease-free and endemic equilibria for the systemand their relation to the basic reproduction number of the disease. The basic reproductionnumber is a very important threshold in mathematical epidemiology measuringthe numbers of secondary infection of the disease following the introduction of a singleinfection in a totally susceptible population. It is a function of demographical andepidemiological parameters. Controlling the transmission of the disease is basicallycontrolling this basic reproduction number to have the value below one by giving certaintreatment to the agent or the vector or the disease as well as to the population.Throughout the discussion we will assume that the control takes part as a vaccinationto susceptible population. In this regards, we discuss the minimum level of vaccinationwhich able to eradicate the disease for various vaccination strategies. To increasethe realism of the model, in the second part of the chapter we discuss the transmissionof dengue by considering the existence of more than one strain of dengue viruses andalso take into account the known ice-berg phenomenon by classifying infected humaninto asymptomatic/mild and severe infection. Some recommendations on the safe andscientifically-sound vaccination strategy and also the directions for further investigationon dengue transmission modeling are provided to conclude the chapter. © 2010 Nova Science Publishers, Inc. All rights reserved.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Basic reproduction number,One-strain and two-strain viruses,Vaccination strategy[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]