A Mathematical Model and Analysis of an SVEIR Model for Streptococcus Pneumonia with Saturated Incidence Force of Infection

SummaryA mathematical model was used to estimate malaria transmission rates based on serological data. The model is minimally stochastic and assumes an age-dependent force of infection for malaria. The transmission rates estimated were applied to a simple compartmental model in order to mimic the malaria transmission.The model has shown a good retrieving capacity for serological and parasite prevalence data.

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Malaria prevalence amongst Brazilian Indians assessed by a new mathematical model

Epidemiology and Infection ◽

10.1017/s0950268800057253 ◽

1993 ◽

Vol 111 (3) ◽

pp. 525-538 ◽

Cited By ~ 6

Author(s):

M. N. Burattini ◽

E. Massad ◽

F. A. B. Coutinho ◽

R. G. Baruzzi

Keyword(s):

Mathematical Model ◽

Control Strategies ◽

Age Distribution ◽

Malaria Prevalence ◽

Reproductive Rate ◽

Force Of Infection ◽

Age Related ◽

Serological Data

SummaryAn alternative way to estimate the endemic level of malaria amongst Brazilian indians is proposed. This is achieved by estimating the age-related “force of infection’ of malaria (the effective inoculation rate), applying a mathematical model, described elsewhere, to serological data. In addition we present a way to estimate the Basic Reproductive Rate of malaria in the same area. The results have shown a good degree of accuracy in describing the endemic pattern of malaria in the area, and also indicate some relevant aspects of its age distribution related to the design of control strategies.

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Stability Analysis of an Epidemic Model with Infected Immigrants and Optimal Vaccination

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b1566.078219 ◽

2019 ◽

Vol 8 (2) ◽

pp. 3071-3077

Keyword(s):

Mathematical Model ◽

Stability Analysis ◽

Epidemic Model ◽

Susceptible Individual ◽

Susceptible Population ◽

Vaccination Strategies ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

The Impact ◽

Disease Free

In this paper an SIR (Susceptible-infectious-recovered) epidemic model consisting of saturated incidence rate with vaccination to the susceptible individual in presence of infected immigrants is studied. Stabilities of disease free and endemic equilibrium are also analyzed. The impact of the infected immigrants in the spread of the illness in a populace is examined. A mathematical model has been used to investigate the inflow of the infected immigrants in a population who rapidly transmit the disease. By using appropriate vaccine level to the susceptible population, disease can be reduced. The main purpose of this work is minimizing the invectives and maximizes the recovered individuals. To attain this, apply optimal vaccination strategies by utilizing the pontryagin’s maximum principle (PMP). Speculative results are demonstrated through the numerical simulations

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Measles elimination in Italy: projected impact of the National Elimination Plan

Epidemiology and Infection ◽

10.1017/s0950268804003152 ◽

2004 ◽

Vol 133 (1) ◽

pp. 87-97 ◽

Cited By ~ 8

Author(s):

P. MANFREDI ◽

J. R. WILLIAMS ◽

M. L. CIOFI DEGLI ATTI ◽

S. SALMASO

Keyword(s):

Mathematical Model ◽

Vaccination Coverage ◽

Measles Vaccine ◽

Demographic Situation ◽

Force Of Infection ◽

Measles Elimination ◽

Catch Up ◽

The Impact ◽

Below Replacement Fertility

A mathematical model was used to evaluate the impact of the Italian Measles National Elimination Plan (NEP), and possible sources of failure in achieving its targets. The model considered two different estimates of force of infection, and the possible effect on measles transmission of the current Italian demographic situation, characterized by a below-replacement fertility. Results suggest that reaching all NEP targets will allow measles elimination to be achieved. In addition, the model suggests that achieving elimination by reaching a 95% first-dose coverage appears unlikely; and that conducting catch-up activities, reaching high vaccination coverage, could interrupt virus circulation, but could not prevent the infection re-emerging before 2020. Also, the introduction of the second dose of measles vaccine seems necessary for achieving and maintaining elimination. Furthermore, current Italian demography appears to be favourable for reaching elimination.

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Sensitivity Analysis of Mathematical Model for Malaria Transmission with Saturated Incidence Rate

Journal of Scientific Research and Reports ◽

10.9734/jsrr/2019/46131 ◽

2019 ◽

Vol 22 (3) ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Mojeeb AL-Rahman EL-Nor Osman ◽

Appiagyei Ebenezer ◽

Nada Abdelsamad Hassan ◽

Cuihong Yang

Keyword(s):

Mathematical Model ◽

Sensitivity Analysis ◽

Malaria Transmission ◽

Incidence Rate ◽

Saturated Incidence Rate ◽

Saturated Incidence

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Analisis Kestabilan dan Kontrol Optimal Model Matematika Partisipasi Pemilih pada Pemilihan Umum dengan Saturated Incidence Rate

Contemporary Mathematics and Applications (ConMathA) ◽

10.20473/conmatha.v3i1.26939 ◽

2021 ◽

Vol 3 (1) ◽

pp. 19

Author(s):

Dinda Ariska Putri ◽

Windarto Windarto ◽

Cicik Alfiniyah

Keyword(s):

Mathematical Model ◽

Incidence Rate ◽

Control Variable ◽

Endemic Equilibrium ◽

Voter Participation ◽

Awareness Campaign ◽

Control Variables ◽

Political Awareness ◽

Saturated Incidence Rate ◽

Saturated Incidence

Voter participation in general elections is an important aspect of a democratic state structure. Participation is determined by the level of public political awareness, if the level of public political awareness is low, voter participation tends to be passive (Abstinence). A mathematical model approach to voter participation in elections that has been modified to a saturated incidence rate is needed to predict voter participation in future elections. This thesis aims to analyze the stability of the equilibrium point and apply the optimal control variable in the form of an awareness campaign. In the model without control variables, we obtain two equilibriums, namely, the non-endemic equilibrium and the endemic equilibrium. Local stability and the existence of endemic equilibrium depend on the basic reproduction number (R0), where R0=bL/(g+m)m. There is voter participation in elections when R0 < 1 and the absence of voter participation in elections when R0 > 1. We also analyze the sensitivity of parameters to determine which parameters are the most influential in this mathematical model. Furthermore, the application of control variables in the mathematical model of voter participation in elections with saturated incidence rate is determined through the Pontryagin Maximum Principle method. Numerical simulation results show that providing control variables in the form of awareness campaign it is quite effective in minimize the number of the voting population who abstained from election.

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