Growth of RB Population in the Conversion Phase of Chlamydia Life Cycle

Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended period.Available data show only RB units in the infected cells 20 hours post infection(hpi),spanning nearly half way through the development cycle.With data collected every 4 hpi,conversion to the elementary body(EB)form begins abruptly at a rapid rate sometime around 24 hpi.By modeling proliferation and conversion as simple birth and death processes,it has been shown that the optimal strategy for maximizing the total(mean)EB population at host cell lysis time is a bang-bang control qualitatively replicating the observed conversion activities.However,the simple birth and death model for the RB proliferation and conversion to EB deviates in a significant way from the available data on the evolution of the RB population after the onset of RB-to-EB conversion.By working with a more refined model that takes into account a small size threshold eligibility requirement for conversion noted in the available data,we succeed in removing the deficiency of the previous models on the evolution of the RB population without affecting the optimal bang-bang conversion strategy.

Optimal Control for Age Distribution and Weighted Size Competitive Species in a Polluted Environment

In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.

The Inhibitory Degree Between Skeletonema costatum and Dinoflagllate Prorocentrum donghaiense at Different Concentrations of Phosphate and Nitrate/Phosphate Ratios

Interactions between Skeletonema costatum (S. costatum) and Prorocentrum donghaiense (P. donghaiiense) were inves-tigated using bi-algal cultures at different concentrations of phosphate (PO4-P) and nitrate/phosphate (N/P) ratios. Experiments were conducted under P-limited conditions and the Lotka-Volterra mathematical model was used to simulate the growth of S. costatum and P. donghaiense in the bi-algal cultures. Both of these two species were inhibited significantly in bi-algal culture. The results of the simulation showed that the inhibitory degree of S. costaum by P. donghaiense was high when the concentration of PO4-P was low (0.1μmolL-1/2 d), but that of P. donghaiense by S. costaum was high with increased PO4-P supply (0.6μmolL-1/2 d). At low concen-tration of PO4-P (0.1μmolL-1/2 d), or high concentration of PO4-P (0.6μmolL-1/2 d) with high N/P ratio (160), the interactions be-tween S. costatum and P. donghaiense were dependent on the initial cell densities of both species. At high concentration of PO4-P (0.6μmolL-1/2 d) with low N/P ratio (25 or 80), S. costatum exhibited a survival strategy superior to that of P. donghaiense. The de-gree of inhibition of P. donghaiense by S. costaum increased with elevated N/P ratio when the medium was supplemented with con-centration 0.1μmolL-1/2 d of PO4-P. The degree of inhibition to P. donghaiense by S. costaum increased with elevated N/P ratio at low concentration of PO4-P (0.1 μmolL-1/2 d). This trend was conversed at high concentration of PO4-P (0.6μmolL-1/2 d). However, the degree of inhibition of S. costaum by P. donghaiense increased with the increased N/P ratio at different PO4-P concentrations (0.1μmolL-1/2 d and 0.6μmolL-1/2 d). These results suggested that both phosphate concentration and N/P ratio affected the competition between S. costaum and P. donghaiense: P. donghaiense is more competitive in environments with low phosphate or high N/P ratio and the influence of N/P ratio on the competition was more significant with lower phosphate concentration.