### Journals Information

Mathematics and Statistics Vol. 9(2), pp. 199 - 207
DOI: 10.13189/ms.2021.090215
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## The Seasonal Reproduction Number of p.vivax Malaria Dynamics in Korea

Anne M. Fernando 1, Ana Vivas Barber 1,*, Sunmi Lee 2
1 Department of Mathematics, Norfolk State University, Norfolk, 23504, Virginia, United States
2 Department of Applied Mathematics, Kyung Hee University, Yongin-si, 446-701, Republic of Korea

ABSTRACT

Understanding the dynamics of Malaria can help in reducing the impact of the disease. Previous research proved that including animals in the human transmission model, or 'zooprophylaxis', is effective in reducing transmission of malaria in the human population. This model studies plasmodium vivax malaria and has variables for animal population and mosquito attraction to animals. The existing time-independent Malaria population ODE model is extended to time-dependent model with the differences explored. We introduce the seasonal mosquito population, a Gaussian profile based on data, as a variant for the previous models. The seasonal reproduction number is found using the next generation matrix, endemic and stability analysis is carried out using dynamical systems theory. The model includes short and long term human incubation periods and sensitivity analysis on parameters and all simulations are over three year period. Simulations show for each year larger peaks in the infected populations and seasonal reproduction number during the summer months and we analyze which parameters have more sensitivity in the model and in the seasonal reproduction number. Analysis provides conditions for disease free equilibrium (DFE) and the system is found to be locally asymptotically stable around the DFE when R0<1, furthermore we find the uniqueness of the endemic equilibrium point. The sensitivity analysis for the parameters shows that the model was not sensitive to the exact values of the long or short term periods as it was to the average number of contacts between host and mosquito or rate of disease progression for mosquitoes. This model shows that inclusion of variable mosquito population informs how domestic animals in the human population can be more effectively used as a method of reducing the transmission of malaria. The most relevant contribution of this work is including the time evolution of mosquito population and simulations show how this feature affects human infection dynamics. An analytical expression for the endemic equilibrium point is provided for future work to establish conditions over which an epidemic may be prevented.

KEYWORDS
Malaria, Long and Short Incubation Period, The Seasonal Reproduction Number, Stability Analysis, Endemic Equilibrium

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Anne M. Fernando , Ana Vivas Barber , Sunmi Lee , "The Seasonal Reproduction Number of p.vivax Malaria Dynamics in Korea," Mathematics and Statistics, Vol. 9, No. 2, pp. 199 - 207, 2021. DOI: 10.13189/ms.2021.090215.

(b). APA Format:
Anne M. Fernando , Ana Vivas Barber , Sunmi Lee (2021). The Seasonal Reproduction Number of p.vivax Malaria Dynamics in Korea. Mathematics and Statistics, 9(2), 199 - 207. DOI: 10.13189/ms.2021.090215.