Volume 5, Issue 6
Mathematical Modelling of Malaria with Treatment

Mini Ghosh

Adv. Appl. Math. Mech., 5 (2013), pp. 857-871.

Published online: 2013-05

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  • Abstract

This paper proposes a Susceptible-Infective-Susceptible (SIS) model to study the malaria transmission with treatment by considering logistic growth of mosquito population. In this work, it is assumed that the treatment rate is proportional to the number of infectives below the capacity and is constant when the number of infectives is greater than the capacity. We find that the system exhibits backward bifurcation if the capacity is small and it gives bi-stable equilibria which makes the system more sensitive to the initial conditions. The existence and stability of the equilibria of the model are discussed in-detail and numerical simulations are presented to illustrate the numerical results.

  • Keywords

Malaria treatment simulation

  • AMS Subject Headings

92D30 37N25

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-857, author = {Mini Ghosh}, title = {Mathematical Modelling of Malaria with Treatment}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {6}, pages = {857--871}, abstract = {

This paper proposes a Susceptible-Infective-Susceptible (SIS) model to study the malaria transmission with treatment by considering logistic growth of mosquito population. In this work, it is assumed that the treatment rate is proportional to the number of infectives below the capacity and is constant when the number of infectives is greater than the capacity. We find that the system exhibits backward bifurcation if the capacity is small and it gives bi-stable equilibria which makes the system more sensitive to the initial conditions. The existence and stability of the equilibria of the model are discussed in-detail and numerical simulations are presented to illustrate the numerical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m12137}, url = {http://global-sci.org/intro/article_detail/aamm/100.html} }
TY - JOUR T1 - Mathematical Modelling of Malaria with Treatment AU - Mini Ghosh JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 857 EP - 871 PY - 2013 DA - 2013/05 SN - 5 DO - http://dor.org/10.4208/aamm.12-m12137 UR - https://global-sci.org/intro/aamm/100.html KW - Malaria KW - treatment KW - simulation AB -

This paper proposes a Susceptible-Infective-Susceptible (SIS) model to study the malaria transmission with treatment by considering logistic growth of mosquito population. In this work, it is assumed that the treatment rate is proportional to the number of infectives below the capacity and is constant when the number of infectives is greater than the capacity. We find that the system exhibits backward bifurcation if the capacity is small and it gives bi-stable equilibria which makes the system more sensitive to the initial conditions. The existence and stability of the equilibria of the model are discussed in-detail and numerical simulations are presented to illustrate the numerical results.

Mini Ghosh. (1970). Mathematical Modelling of Malaria with Treatment. Advances in Applied Mathematics and Mechanics. 5 (6). 857-871. doi:10.4208/aamm.12-m12137
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