Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of co More
Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of control measures and then examine the effect of the control strategies on the transmission dynamics of Tungiasis. The model effective reproduction number is determined using the next generation operator method and the analysis is performed using the stability theory of the differential equations. The analytical results show that the disease free equilibrium is locally asymptotically stable when and unstable when . Using Meltzer matrix stability theorem we found that the disease free equilibrium is globally asymptotically stable and by Lyapunov method, the endemic equilibrium is globally asymptotically stable when . From the numerical simulation it was observed that the control strategies have positive impact on the reduction of transmission of Tungiasis disease and that they work better in combination than when applied as singly. The results from simulations will help the decision makers from national health care to advise people at risk with Tungiasis to apply the control strategies based on: educational campaign, personal protection, personal treatment, environmental hygiene and insecticides application to control the flea.
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Optimum cropping pattern in vineyard irrigated farming is one of the vital tasks for obtaining the best irrigation water reserves of the command. In this article the linear programming model was developed for optimal use of water and land resources. The model was tested More
Optimum cropping pattern in vineyard irrigated farming is one of the vital tasks for obtaining the best irrigation water reserves of the command. In this article the linear programming model was developed for optimal use of water and land resources. The model was tested by the data from Chinangali irrigated farmland with 120 cultivated hectares found in Dodoma, Tanzania. The results show that, the savings of 16 470.40 m3 of water per annum will be observed if the planting of 14.18 hectares of Chardonnay, 27.97 hectares of Cabernet sauvignon, 56.14 hectares of Riesling and 21.39 hectares of Chenin blanc. Thus, it was recommended that 1 173 359.60 m3 of water should be released to the irrigated farmland per annum for the best irrigation planning versus the 1 189 830 m3 of water supplied currently per annum.
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