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- 2020| SCIK Publishing Corp...This article suggested and analyzed the transmission dynamics of malaria disease in a population using a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control strategies on the infected individuals in the population can be determined. The possible influence of exploring a single control, the combination of two, and the three controls on the spread of the disease was also investigated. Numerical simulation was carried out and pertinent findings are displayed graphically.
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- Malaria remains a significant global health problem; with the potential for developing resistance to conventional antimalarials justifying novel therapeutic approaches. This study investigates the potential of microalgal metabolites as dual-inhibitors of Plasmodium falciparum glutathione S-transferase (PfGST) and apical membrane antigen 1 (AMA1); two of the most important proteins in parasite survival and host cell invasion. By high-throughput molecular docking simulations; we studied binding energy distributions; conformational characteristics by principal component analysis; pharmacophoric and pharmacokinetic research with structure-activity relationships of its inhibitors. Our findings indicate various patterns of interactions: PfGST exhibits a unimodal distribution of binding energy with a maximum at -7.2 kcal/mol; whereas AMA1 exhibits a bimodal distribution with minimum at -6.8 and − 8.3 kcal/mol; suggesting various mechanisms of binding. Specifically; platencin was among the most potent dual-inhibitors with binding energies of -7.30 kcal/mol to PfGST and − 8.20 kcal/mol to AMA1. Pharmacophoric characteristics were found to be the hydrogen-bond acceptors; hydrophobic centers; and aromatic rings as determinants of dual-target activity; the optimal dual-target inhibitory potential occurring with compounds of balanced physicochemical properties. High-resolution molecular interaction mapping validated that while the two targets identify overlapping classes of interactions with the metabolites; PfGST interaction is dominated by hydrophobic contacts and AMA1 exploits higher electrostatic complementarity and hydrogen-bonding networks. ADMET profiling also revealed favorable drug-likeness in dual-inhibitory compounds of intermediate molecular size (420–500 Da) and moderate lipophilicity (LogP 3–6). This study provides a structural basis for rationale design of antimalarial compounds from microalgal metabolites. Our findings confirm the conformational selection hypothesis; in which these compounds selectively bind to and stabilize protein conformations that inhibit parasite function; possibly circumventing known resistance mechanisms.
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- In this paper, the integrability of a nonlinear system developing endemic Malaria was demonstrated using Prelle–Singer techniques. In addition, Lie symmetry techniques were employed to identify additional independent variables that led to the modification of the nonlinear model and the development of analytical solutions.
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- Malaria is a mosquito-borne disease spread by an infected vector (infected female Anopheles mosquito) or through transfusion of plasmodium-infected blood to susceptible individuals. The disease burden has resulted in high global mortality, particularly among children under the age of five. Many intervention responses have been implemented to control malaria disease transmission, including blood screening, Long-Lasting Insecticide Bed Nets (LLIN), treatment with an anti-malaria drug, spraying chemicals/pesticides on mosquito breeding sites, and indoor residual spray, among others. As a result, the SIR (Susceptible—Infected—Recovered) model was developed to study the impact of various malaria control and mitigation strategies. The associated basic reproduction number and stability theory is used to investigate the stability analysis of the model equilibrium points. By constructing an appropriate Lyapunov function, the global stability of the malaria-free equilibrium is investigated. By determining the direction of bifurcation, the implicit function theorem is used to investigate the stability of the model endemic equilibrium. The model is fitted to malaria data from Benue State, Nigeria, using R and MATLAB. Estimates of parameters were made. Following that, an optimal control model is developed and analyzed using Pontryaging's Maximum Principle. The malaria-free equilibrium point is locally and globally stable if the basic reproduction number (R0) and the blood transfusion reproduction number (Rα) are both less or equal to unity. The study of the sensitive parameters of the model revealed that the transmission rate of malaria from mosquito-to-human (βmh), transmission rate from humans-to-mosquito (βhm), blood transfusion reproduction number (Rα) and recruitment rate of mosquitoes (bm) are all sensitive parameters capable of increasing the basic reproduction number (R0) thereby increasing the risk in spreading malaria disease. The result of the optimal control shows that five possible controls are effective in reducing the transmission of malaria. The study recommended the combination of five controls, followed by the combination of four and three controls is effective in mitigating malaria transmission. The result of the optimal simulation also revealed that for communities or areas where resources are scarce, the combination of Long Lasting Insecticide Treated Bednets (u2), Treatment (u3), and Indoor insecticide spray (u5) is recommended. Numerical simulations are performed to validate the model's analytical results.
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