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Frequency Dependent Incidence Model for Acute and Chronic Schistosomiasis

100%
Derick N., Onuorah M. O.
World News of Natural Sciences
|
2019
|
vol. 23
276-296
EN
In this research work, a deterministic mathematical model for schistosomiasis transmission dynamics is presented. The model consists of five non-liniar ordinary differential equations incorporating the acute and chronic infectious compartments. The basic reproductive number, (the number of secondary infections when a single infectious individual is introduced into a population where everyone is susceptible) was obtained. Furthermore, we gained and analyzed for stability, the disease-free and endemic equilibrium. The qualitative feature of the model shows that the long-term behavior of the model is independent of initial conditions. Numerical simulation of the various state variables were obtained using matlab software.
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Mathematical Modeling of Control Strategies for Visceral leishmaniasis

84%
Onyekwelu O. M., Baker N.
World News of Natural Sciences
|
2021
|
vol. 37
102-116
EN
In this paper, a deterministic mathematical model for the transmission dynamics of Visceral leishmaniasis (VL) was formulated and analyzed. The basic reproductive number R0 was obtained using the next generation matrix method. The model which was parameterized using the 2011 cases of Visceral Leishmaniasis in South Sudan, was used to assess two control measures. Numerical simulation reveals that the exposed population is reduced by high detection rate, and low biting rate of sandflies. Further, our model simulation gave the values of the contact rate of susceptible human, α1 and the detection rate of new cases, σ at which the basic reproductive number is less than one, (R0 < 1), equal to one (R0 = 1) and greater than one (R0 > 1).
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