Asymptotic profiles of the endemic equilibrium of a diffusive SIS epidemic system with saturated incidence rate and spontaneous infection

Schistosomiasis is a disease caused by infections of the genus Schistosoma. Schistosomiasis can be transmitted through schistosoma worms that contact human skin. Schistosomiasis is a disease that continues to increase in spread. Saturated incidence rates pay attention to the ability to infect a disease that is limited by an increase in the infected population. This thesis formulates and analyzes a mathematical model of the distribution of schistosomiasis with a saturated incidence rate. Based on the analysis of the model, two equilibrium points are obtained, namely non-endemic equilibrium points (E0) and endemic equilibrium points (E1). Both equilibrium points are conditional asymptotically stable. The nonendemic equilibrium point will be asymptotically stable if rh > dh, rs > ds and R0 < 1, while the endemic equilibrium point will be asymptotically stable if R0 > 1. Sensitivity analysis shows that there are parameters that affect the spread of the disease. Based on numerical simulation results show that when R0 < 1, the number of infected human populations (Hi), the number of infected snail populations (Si), the amount of cercaria density (C) and the amount of miracidia density (M) will tend to decrease until finally extinct. Otherwise at the time R0 > 1, the number of the four populations tends to increase before finally being in a constant state.

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DYNAMICS OF AN SIS EPIDEMIC MODEL WITH A SATURATED INCIDENCE RATE UNDER TIME DELAY AND STOCHASTIC INFLUENCE

International Journal of Pure and Apllied Mathematics ◽

10.12732/ijpam.v112i4.4 ◽

2017 ◽

Vol 112 (4) ◽

Author(s):

R. Kumar G. ◽

L. Narayan K. ◽

R. Reddy B.

Keyword(s):

Time Delay ◽

Incidence Rate ◽

Epidemic Model ◽

Sis Epidemic Model ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Sis Epidemic

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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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