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Malaria is an infectious disease caused by the Plasmodium parasite, and transmitted amongst humans through the bites of the female Anopheles mosquito. In this work, we used a system of nonlinear ordinary differential equations to model the disease. The new model incorporated vaccination, treatment and vector control using sterile-insect technology (SIT). Through stability analysis, we showed that the malaria-free equilibrium (MFE) point is locally and globally asymptotically stable (GAS) when the malaria control number, $R_m$ is less than one, and unstable otherwise. The global stability of the MFE is an indication that there exists a unique endemic equilibrium point in the system and the absence of backward bifurcation in the model. The existence of the endemic equilibrium is shown and seen to be GAS. The work also showed the effects of treatment, vaccination and vector control in controlling malaria. Also, sensitivity analysis of important model parameters were shown. The result showed that effective treatment of infectious humans with malaria helps to reduce the spread of the disease in human and mosquito populations, respectively. Vaccination played a vital role in protecting humans from being infected thus reducing the spread of the disease. SIT significantly reduced the population of mosquitoes and the spread of malaria. Hence, we conclude that effective control of the spread of malaria requires measures that help control the disease in both human and mosquito populations as shown in this work. Plots were presented to show the dynamics of the disease.

Artemisinin and its derivatives (ARTs), due to their potent antimalarial activities, are widely used as frontline antimalarials across the world. Although the large-scale deployment of ARTs has significantly contributed to a substantial decline in malaria deaths, the global malaria burden is still high. New antimalarial treatments need to be developed to manage the growing artemisinin resistance. Understanding the status of ART development is crucial for developing strategies for new alternatives and identifying opportunities to develop ART-based treatments. This study sampled ART clinical trials from the past two decades to gain an overview of the global ART-development landscape. A total of 768 trials were collected to analyze the disease focuses, activity trends, development status, geographic distribution, and combination treatment profiles of ART trials. The findings highlighted the constant focus of ARTs on malaria, the evolving combination research focus, the distinctions between ART development preferences across global regions, the urgent demands for treatments for artemisinin-resistant malaria, and the unavoidable need to consider ART combinations in the development of new antimalarials.

In this paper, we develop a mathematical model to assess the strength of the effects of catastrophic anemia level on the dynamical transmission of malaria parasite within the body of a host. We first consider a temporal model. The important mathematical features of the model are thoroughly investigated. We found that the model exhibits forward bifurcation. We also consider a spatiotemporal model using reaction–diffusion equations. The model is numerically analyzed to assess the impact of anemia on the dynamical transmission of malaria parasite within the body of a host. Through numerical simulation, we found that malaria can lead to a catastrophic anemia level even if the parasite is nonpersistent within the body of a host. Numerical results also suggest that to reduce or control the anemia level, the strategy should be to accelerate innate cell reproduction rate or should have the ability to clean parasitized red blood cells (PRBCs) with a high mortality rate.

Recent experimental results have implied that Serratia AS1 bacteria efficiently suppress the development of P. falciparum, and rapidly disseminate via vertical transmission and sexual transmission throughout mosquito population. In this paper, we propose a new malaria model to investigate the roles of saturated treatment and AS1 bacteria in malaria transmission. One feature of the model is that human and mosquito populations dynamics run on disparate temporal scales. Singular perturbation techniques are used for the separation of fast and slow dynamics. It also enables us to overcome the difficulties of exploring bifurcations in higher dimensional system. We demonstrate that the reduced systems may undergo backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation of codimension 2, which indicates that the delayed effect for treatment has important implications for malaria control. Numerical simulations substantiate these analytical results and show epidemiological insights. Finally, the model without AS1 bacteria transmission is applied to simulate the accumulative malaria cases in Burundi. We observe that malaria may not be eliminated by a single control in Burundi. A variety of available control measures should be adopted to eradicate malaria, such as improving treatment rate, reducing the delayed effect for treatment, and possibly releasing mosquitoes that carry AS1 bacteria.

In this paper, general SIS and SIRS models with immigration of human population for the spread of malaria are proposed and analyzed. Effects of natural as well as human population density related environmental and ecological factors, which are conductive to the survival and growth of mosquito population, are considered. It is shown in both the cases that as the parameters governing environmental and ecological factors increase, the spread of malaria increases. It is also found that due to immigration, this infectious disease becomes more endemic.

Approximately one-third of the world's population that is at risk to malaria lives in India. Plasmodium falciparum, a deadly form of malaria, accounts for about 50% of the cases there. Since 1940s, India has used a number of programs to combat the disease with variable success. Since 1998, the total numbers of malaria cases, and in particular P. falciparum cases, have been steadily declining, making India one of the success stories among the countries supported by the Roll Back Malaria (RBM) Partnership. This article considers India's P. falciparum control methods from the perspective of a Ross-MacDonald type model. The model is fitted to the P. falciparum cases in India over the period 1983–2009. We focus on the disease reproduction number as being a measure of success of programs. Before the start of RBM measures, the disease reproduction number was , meaning that the incidence of disease was increasing among the population. With the new control measures , suggesting that P.falciparum cases may be declining to zero but extremely slowly. The model here projects 0.734 million cases of P. falciparum malaria for 2010, down from 1.14 million cases in 2000. This impressive 36% decrease falls somewhat short of the RBM's goal of 50% reduction. However, a sensitivity analysis of the disease reproduction number done here suggests that India's control programs do apply controls at the most critical points in the disease cycle; namely, mosquito biting rates, mosquito mortality, and treatment of infected humans. This suggests that as more resources become available, they should be applied to strengthen these controls. The novelty here is in fitting recent data on malaria from India to derive current values of the disease reproduction number.

Vector control and pharmaceutical treatments are currently the main methods of malaria control. To assess their impacts on disease transmission and prevalence, sensitivity and optimal control analysis are performed respectively on a mathematical malaria model. Comparisons are made between the result of sensitivity analysis and that of optimal control analysis. Numerical simulation shows that optimal control strategy is available and cost-efficient. The simulating results also indicates that vector control is always much more beneficial than other anti-malaria measures in an optimal control programme. This further suggests that the results of sensitivity analysis by calculating sensitivity indices cannot help policy-makers to formulate a more effective optimal control programme.

An age-structured mathematical model for malaria is presented. The model explicitly includes the human and mosquito populations, structured by chronological age of humans. The infected human population is divided into symptomatic infectious, asymptomatic infectious and asymptomatic chronic infected individuals. The original partial differential equation (PDE) model is reduced to an ordinary differential equation (ODE) model with multiple age groups coupled by aging. The basic reproduction number is derived for the PDE model and the age group model in the case of general n age groups. We assume that infectiousness of chronic infected individuals gets triggered by bites of even susceptible mosquitoes. Our analysis points out that this assumption contributes greatly to the expression and therefore needs to be further studied and understood. Numerical simulations for n = 2 age groups and a sensitivity/uncertainty analysis are presented. Results suggest that it is important not only to consider asymptomatic infectious individuals as a hidden cause for malaria transmission, but also asymptomatic chronic infections (>60%), which often get neglected due to undetectable parasite loads. These individuals represent an important reservoir for future human infectiousness. By considering age-dependent immunity types, the model helps generate insight into effective control measures, by targeting age groups in an optimal way.

Malaria is a life-threatening disease caused by parasites that are transmitted to people through the bites of infected mosquitoes. In this paper, a deterministic model for malaria transmission, that incorporates superinfection is presented. Qualitative analysis of the model reveals the presence of backward bifurcation in which a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. Optimal control theory is then applied to the model to study time-dependent treatment efforts to minimize the infected in individuals while keeping the implementation cost at a minimum.

A new mechanistic deterministic model for assessing the impact of temperature variability on malaria transmission dynamics is developed. Sensitivity and uncertainty analyses of the model parameters reveal that, for temperature values in the range 16–$34^{\circ }$C, the three parameters with the greatest influence on disease dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes and human recruitment rate. This study emphasizes the combined use of mosquito-reduction strategies and personal protection against mosquito bites during periods when the mean monthly temperatures are in the range 16.7–25${}^{\circ }$C. For higher monthly mean temperatures in the range 26–34${}^{\circ }$C, mosquito-reduction strategies should be emphasized ahead of personal protection. Numerical simulations of the model reveal that mosquito maturation rate has a minimum sensitivity (to the associated reproduction threshold of the model) at 24${}^{\circ }$C and maximum at 30${}^{\circ }$C. The mosquito biting rate has maximum sensitivity at 26${}^{\circ }$C, while the minimum value for the transmission probability per bite for susceptible mosquitoes occurs at 24${}^{\circ }$C. Furthermore, it is shown, using mean monthly temperature data from 67 cities across the four regions of sub-Saharan Africa, that malaria burden (measured in terms of the total number of new cases of infection) increases with increasing temperature in the range 16–28${}^{\circ }$C and decreases for temperature values above 28${}^{\circ }$C in West Africa, 27${}^{\circ }$C in Central Africa, 26${}^{\circ }$C in East Africa and 25${}^{\circ }$C in South Africa. These findings, which support and complement a recent study by other authors, reinforce the potential importance of temperature and temperature variability on future malaria transmission trends. Further simulations show that mechanistic malaria transmission models that do not incorporate temperature variability may under-estimate disease burden for temperature values in the range 23–27${}^{\circ }$C, and over-estimate disease burden for temperature values in the ranges 16–22${}^{\circ }$C and 28–32${}^{\circ }$C. Additionally, models that do not explicitly incorporate the dynamics of immature mosquitoes may under- or over-estimate malaria burden, depending on mosquito abundance and mean monthly temperature profile in the community.

This study presents a new mathematical model for assessing the impact of sterile insect technology (SIT) and seasonal variation in local temperature on the population abundance of malaria mosquitoes in an endemic setting. Simulations of the model, using temperature data from Kipsamoite area of Kenya, show that a peak abundance of the mosquito population is attained in the Kipsamoite area when the mean monthly temperature reaches $30^{\circ }\mathrm{\text{C}}$. Furthermore, in the absence of seasonal variation in local temperature, our results show that releasing more sterile male mosquitoes (e.g., 100,000) over a one year period with relatively short duration between releases (e.g., weekly, bi-weekly or even monthly) is more effective than releasing smaller numbers of the sterile male mosquitoes (e.g., 10,000) over the same implementation period and frequency of release. It is also shown that density-dependent larval mortality plays an important role in determining the threshold number of sterile male mosquitoes that need to be released in order to achieve effective control (or elimination) of the mosquito population in the community. In particular, low(high) density-dependent mortality requires high(low) numbers of sterile male mosquitoes to be released to achieve such control. In the presence of seasonal variation in local temperature, effective control of the mosquito population using SIT is only feasible if a large number of the sterile male mosquitoes (e.g., 100,000) is periodically released within a very short time interval (at most weekly). In other words, seasonal variation in temperature necessitates more frequent releases (of a large number) of sterile male mosquitoes to ensure the effectiveness of the SIT intervention in curtailing the targeted mosquito population.

In this paper, a mathematical model for malaria-dysentery co-infection was formulated in order to study and examine its dynamic relationship in the presence of malaria and dysentery preventive and treatment measures. First, analysis of the single infection steady states was done and then the basic reproduction number was obtained. Furthermore, investigation into the existence and stability of equilibria carried out. The single infection models were found to exhibit the possibility of backward bifurcation. Thereafter, the impact of malaria on the dynamics of dysentery is further investigated. Second, incorporating time-dependent controls, using Pontryagin’s Maximum Principle, the necessary conditions for the optimal control of the disease was derived. It is found that malaria infection may be associated with an increased risk of dysentery. Also, that dysentery infection may be associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time it also includes effective prevention and control measures for dysentery. Policy makers should take efforts on preventive strategies in combating dysentery and malaria.

In this paper, we proposed and analyzed a nonlinear deterministic model for the impact of temperature variability on the epidemics of the malaria. The model analysis showed that all solutions of the systems are positive and bounded with initial conditions in a certain set. Thus, the model is proved to be both epidemiologically meaningful and mathematically well-posed. Using the next-generation matrix approach, the basic reproduction number with respect to the disease-free equilibrium (DFE) point is obtained. The local stability of the equilibria points is shown using the Routh–Hurwitz criterion. The global stability of the equilibria points is performed using the Lyapunov function. Also, we proved that if the basic reproduction number is less than one, the DFE is locally and globally asymptotically stable. But, if the basic reproduction number is greater than one, the unique endemic equilibrium exists, locally and globally asymptotically stable. The sensitivity analysis of the parameters is also described. Moreover, we used the method implemented by the center manifold theorem to identify that the model exhibits forward and backward bifurcations. From our analytical results, we confirmed that the variation of temperature plays a significant role on the transmission of malaria. Lastly, numerical simulations are demonstrated to enhance the analytical results of the model.

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The article is about single cell mechanics and its connection to human diseases. It touches on the biomechanics used to perform quantitative study in the physical properties of cells with the progression of certain diseases such as malaria, sickle cell anemia and cancer.