Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence

This paper presents the mathematical analysis of the dynamical system for avian influenza.The proposed model considers a nonlinear dynamical model of birds and human.The half-saturated incidence rate is used for the transmission of avian influenza infection.Rigorous mathematical results are presented for the proposed models.The local and global dynamics of each model are presented and proven that when R0<1,then the disease-free equilibrium of each model is stable both locally and globally,and when R0>1,then the endemic equilibrium is stable both locally and globally.The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.

Effects of Nitrogen Sources and Concentrations on the Growth of Different Phytoplankton Taxa

Effects of different nitrogen(N)compounds and concentrations on the growth of the three different phytoplankton taxa,Skeletonema costatum(Bacillariophyceae),Prorocentrum micans(Dinophyceae),and Chattonella marina(Raphidophyceae),were investigated.The Monod equation was applied to examine effects of N concentrations on the growth of algal cells.Results showed that nitrate(NO_(3)-N)and urea served as good N sources for the three phytoplankton taxa.S.costatum grew well on all of the seven N sources.C.marina can effectively use the two amino acids,glycine(Gly)and serine(Ser),however cannot utilize alanine(Ala),threonine(Thr),and asparaginic acid(Asp).P.micans cannot grow in five amino acid substrates.All of the three phytoplankton taxa grew well under different proportions of urea-N,and C.marina grew significantly better in medium with both NO_(3)-and urea-N.The values of maximum growth rate(μmax)and half-saturation nutrient concentration(KS)for NO_(3)-N were 0.71 divisions d−1 and 53.55μmolL^(−1) for S.costatum,0.67 divisions d−1 and 23.31μmolL^(−1) for P.micans,and 0.23 divisionsd−1 and 17.57μmolL^(−1) for C.marina,respectively.The results suggested that S.costatum had a high N demand for growth,and was capable of using wide ranges of N compounds.The strategy of N utilization for S.costatum may make this species an advantage in N-enriched sea areas especially the dissolved organic nitrogen(DON)rich coastal waters,which might be the reason why S.costatum widely distributes in the cosmo-politan coastal and estuarine sea areas.

Transmission dynamics and control strategies assessment of avian influenza A(H5N6)in the Philippines

Due to the outbreaks of Highly Pathogenic Avian Influenza A(HPAI)H5N6 in the Philippines(particularly in Pampanga and Nueva Ecija)in August 2017,there has been an increase in the need to cull the domestic birds to control the spread of the infection.However,this control method poses a negative impact on the poultry industry.In addition,the pathogenicity and transmissibility of the H5N6 in both the birds and the humans remain largely unknown which call for the necessity to develop more strategic control methods for the virus.In this study,we constructed a mathematical model for the bilinear and half-saturated incidence to compare their corresponding effect on transmission dynamics of H5N6.The simulations of half-saturated incidence model were similar to what occurred during the H5N6 outbreak(2017)in the Philippines.Instead of culling the birds,we implemented other control strategies such as non-medicinal(personal protection and poultry isolation)and medicinal(poultry vaccination)ways to prevent,reduce,and control the rate of the H5N6 virus transmission.Among the proposed control strategies,we have shown that the poultry isolation strategy is still the most effective in reducing the infected birds.

Seasonal dependency of controlling factors on the phytoplankton production in Taihu Lake, China

In this study, 44 profiles of gross primary productivity(GPP) and sunlight, along with water temperature, Chlorophyll-a(Chla) and nutrients, were observed in Meiliang Bay of Taihu Lake, China, in the spring, summer, and fall seasons. Effects of water temperature, light,and nutrient concentration were examined in relation to the GPP-unit-Chla(GPP of algae per Chla). The results showed that the optimum temperature for the GPP of phytoplankton was 27.9°C, the optimal PNA-unit-Chla(photon number absorbed by phytoplankton per Chla) was 0.25(mol), and the HSCN-unit-Chla and HSCP-unit-Chla(half-saturation constants of nitrogen and phosphorus of algae per Chla) were 0.005(mg/L) and 0.0004(mg/L), respectively. The seasonal dependency of the effect of different factors on the GPP was analyzed. Compared with temperature and nutrients, light was found to be the most important factor affecting the GPP during the three seasons. The effect of temperature and nutrients on the GPP of phytoplankton has obvious seasonal change. In spring, temperature was the secondary factor affecting the GPP of phytoplankton, and the effect of nutrients may be negligible in the eutrophic lake on account of temperature limit, which showed that the GPP of algae was only affected by the physical process. In summer and fall, temperature didn't affect the GPP of algae, and the presence of nutrients was the secondary factor affecting the GPP of phytoplankton. From summer to fall, effect of phosphorus was weakened and effect of nitrogen was enhanced.