Assessment of Anopheles salivary antigens as individual exposure biomarkers to species-specific malaria vector bites

The development of parasitological immunity against malaria affects the ability to detect infection, the efficiency of the local human parasite reservoir at infecting mosquitoes, and the response to reintroduction of parasites to previously cleared areas. Observations of similar age-trends in detected prevalence and mean parasitaemia across more than an order-of-magnitude of variation in baseline transmission complicate simple exposure-driven explanations. Mathematical models often employ age-dependent immune factors to match the observed trends, while the present model uses a new detailed mechanistic model of parasite transmission dynamics to explain age-trends through the mechanism of parasite diversity. Illustrative simulations are performed for multiple field sites in Tanzania and Nigeria, and observed age-trends and seasonality in parasite prevalence are recreated in silico, proffering possible mechanistic explanations of the observational data. Observed temporal dynamics in measured parasitaemia are recreated for each location and age-prevalence outputs are studied. Increasing population-level diversity in malaria surface antigens delays development of broad parasitological immunity. A local parasite population with high diversity can recreate the observed trends in age-prevalence across more than an order of magnitude of variation in transmission intensities. Mechanistic models of human immunity and parasite antigen diversity can recreate the observed temporal patterns for the development of parasitological immunity across a wide range of transmission intensities. This has implications for the distribution of disease burden across the population, the human transmission reservoir, design of elimination campaigns, and development and roll-out of potential vaccines.     

Revisiting the basic reproductive number for malaria and its implications for malaria control

The prospects for the success of malaria control depend, in part, on the basic reproductive number for malaria, R0. Here, we estimate R0 in a novel way for 121 African populations, and thereby increase the number of R0 estimates for malaria by an order of magnitude. The estimates range from around one to more than 3,000. We also consider malaria transmission and control in finite human populations, of size H. We show that classic formulas approximate the expected number of mosquitoes that could trace infection back to one mosquito after one parasite generation, Z0(H), but they overestimate the expected number of infected humans per infected human, R0(H). Heterogeneous biting increases R0 and, as we show, Z0(H), but we also show that it sometimes reduces R0(H); those who are bitten most both infect many vectors and absorb infectious bites. The large range of R0 estimates strongly supports the long-held notion that malaria control presents variable challenges across its transmission spectrum. In populations where R0 is highest, malaria control will require multiple, integrated methods that target those who are bitten most. Therefore, strategic planning for malaria control should consider R0, the spatial scale of transmission, human population density, and heterogeneous biting.     

Malaria vector analysis and control

Antivector measures in malaria control should aim for a cost-effective reduction of the transmission potential ideally to below the critical level for sustained transmission. The available measures include those that decrease vector abundance, vector-human contact and vector survival rate or that increase the length of the sporogonic cycle. These have widely different impact on malaria transmission, as shown by epidemiological modelling. Direct modification of vector receptivity to Plasmodium is also hypothetically attainable by the use of transmission-blocking vaccines or by genetic manipulation and replacement of the vector population. Vector analysis constitutes the essential prerequisite for basic malaria epidemiology as well as for the development, planning and evaluation of antivector measures. The rationale, the problems and the perspectives of vector analysis are reviewed here by Mario Coluzzi, on the basis of his experience with Afrotropical and Mediterranean malaria vectors.     

Development of a new version of the Liverpool Malaria Model. II. Calibration and validation for West Africa

Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease     

Human movement data for malaria control and elimination strategic planning

ABSTRACT: Recent increases in funding for malaria control have led to the reduction in transmission in many malaria endemic countries, prompting the national control programmes of 36 malaria endemic countries to set elimination targets. Accounting for human population movement (HPM) in planning for control, elimination and post-elimination surveillance is important, as evidenced by previous elimination attempts that were undermined by the reintroduction of malaria through HPM. Strategic control and elimination planning, therefore, requires quantitative information on HPM patterns and the translation of these into parasite dispersion. HPM patterns and the risk of malaria vary substantially across spatial and temporal scales, demographic and socioeconomic sub-groups, and motivation for travel, so multiple data sets are likely required for quantification of movement. While existing studies based on mobile phone call record data combined with malaria transmission maps have begun to address within-country HPM patterns, other aspects remain poorly quantified despite their importance in accurately gauging malaria movement patterns and building control and detection strategies, such as cross-border HPM, demographic and socioeconomic stratification of HPM patterns, forms of transport, personal malaria protection and other factors that modify malaria risk. A wealth of data exist to aid filling these gaps, which, when combined with spatial data on transport infrastructure, traffic and malaria transmission, can answer relevant questions to guide strategic planning. This review aims to (i) discuss relevant types of HPM across spatial and temporal scales, (ii) document where datasets exist to quantify HPM, (iii) highlight where data gaps remain and (iv) briefly put forward methods for integrating these datasets in a Geographic Information System (GIS) framework for analysing and modelling human population and Plasmodium falciparum malaria infection movements.     

Heterologous expression of the C-terminal antigenic domain of the malaria vaccine candidate Pfs48/45 in the green algae Chlamydomonas reinhardtii

Malaria is a widespread and infectious disease that is a leading cause of death in many parts of the world. Eradication of malaria has been a major world health goal for decades, but one that still remains elusive. Other diseases have been eradicated using vaccination, but traditional vaccination methods have thus far been unsuccessful for malaria. Infection by Plasmodium species, the causative agent of malaria, is currently treated with drug-based therapies, but an increase in drug resistance has led to the need for new methods of treatment. A promising strategy for malaria treatment is to combine transmission blocking vaccines (TBVs) that prevent spread of disease with drug-based therapies to treat infected individuals. TBVs can be developed against surface protein antigens that are expressed during parasite reproduction in the mosquito. When the mosquito ingests blood from a vaccinated individual harboring the Plasmodium parasite, the antibodies generated by vaccination prevent completion of the parasites life-cycle. Animal studies have shown that immunization with Pfs48/45 results in the production of malaria transmission blocking antibodies; however, the development of this vaccine candidate has been hindered by poor expression in both prokaryotic and eukaryotic hosts. Recently, the chloroplast of Chlamydomonas reinhardtii has been used to express complex recombinant proteins. In this study, we show that the C-terminal antigenic region of the Pfs48/45 antigen can be expressed in the chloroplast of the green algae C. reinhardtii and that this recombinant protein has a conformation recognized by known transmission blocking antibodies. Production of this protein in algae has the potential to scale to the very large volumes required to meet the needs of millions at risk for contracting malaria.     

A Realistic Host-Vector Transmission Model for Describing Malaria Prevalence Pattern

Malaria continues to be a major public health concern all over the world even after effective control policies have been employed, and considerable understanding of the disease biology have been attained, from both the experimental and modelling perspective. Interactions between different general and local processes, such as dependence on age and immunity of the human host, variations of temperature and rainfall in tropical and sub-tropical areas, and continued presence of asymptomatic infections, regulate the host-vector interactions, and are responsible for the continuing disease prevalence pattern. In this paper, a general mathematical model of malaria transmission is developed considering short and long-term age-dependent immunity of human host and its interaction with pathogen-infected mosquito vector. The model is studied analytically and numerically to understand the role of different parameters related to mosquitoes and humans. To validate the model with a disease prevalence pattern in a particular region, real epidemiological data from the north-eastern part of India was used, and the effect of seasonal variation in mosquito density was modelled based on local climactic data. The model developed based on general features of host-vector interactions, and modified simply incorporating local environmental factors with minimal changes, can successfully explain the disease transmission process in the region. This provides a general approach toward modelling malaria that can be adapted to control future outbreaks of malaria.     

Regime shifts and heterogeneous trends in malaria time series from Western Kenya Highlands

Large malaria epidemics in the East African highlands during the mid and late 1990s kindled a stream of research on the role that global warming might have on malaria transmission. Most of the inferences using temporal information have been derived from a malaria incidence time series from Kericho. Here, we report a detailed analysis of 5 monthly time series, between 15 and 41 years long, from West Kenya encompassing an altitudinal gradient along Lake Victoria basin. We found decreasing, but heterogeneous, malaria trends since the late 1980s at low altitudes (<1600 m), and the early 2000s at high altitudes (>1600 m). Regime shifts were present in 3 of the series and were synchronous in the 2 time series from high altitudes. At low altitude, regime shifts were associated with a shift from increasing to decreasing malaria transmission, as well as a decrease in variability. At higher altitudes, regime shifts reflected an increase in malaria transmission variability. The heterogeneity in malaria trends probably reflects the multitude of factors that can drive malaria transmission and highlights the need for both spatially and temporally fine-grained data to make sound inferences about the impacts of climate change and control/elimination interventions on malaria transmission.     

Inference and dynamic simulation of malaria using a simple climate-driven entomological model of malaria transmission

Given the crucial role of climate in malaria transmission, many mechanistic models of malaria represent vector biology and the parasite lifecycle as functions of climate variables in order to accurately capture malaria transmission dynamics. Lower dimension mechanistic models that utilize implicit vector dynamics have relied on indirect climate modulation of transmission processes, which compromises investigation of the ecological role played by climate in malaria transmission. In this study, we develop an implicit process-based malaria model with direct climate-mediated modulation of transmission pressure borne through the Entomological Inoculation Rate (EIR). The EIR, a measure of the number of infectious bites per person per unit time, includes the effects of vector dynamics, resulting from mosquito development, survivorship, feeding activity and parasite development, all of which are moderated by climate. We combine this EIR-model framework, which is driven by rainfall and temperature, with Bayesian inference methods, and evaluate the model’s ability to simulate local transmission across 42 regions in Rwanda over four years. Our findings indicate that the biologically-motivated, EIR-model framework is capable of accurately simulating seasonal malaria dynamics and capturing of some of the inter-annual variation in malaria incidence. However, the model unsurprisingly failed to reproduce large declines in malaria transmission during 2018 and 2019 due to elevated anti-malaria measures, which were not accounted for in the model structure. The climate-driven transmission model also captured regional variation in malaria incidence across Rwanda’s diverse climate, while identifying key entomological and epidemiological parameters important to seasonal malaria dynamics. In general, this new model construct advances the capabilities of implicitly-forced lower dimension dynamical malaria models by leveraging climate drivers of malaria ecology and transmission.     

Environmental Management for Malaria Control: Knowledge and Practices in Mvomero,Tanzania

Environmental conditions play an important role in the transmission of malaria; therefore, regulating these conditions can help to reduce disease burden. Environmental management practices for disease control can be implemented at the community level to complement other malaria control methods. This study assesses current knowledge and practices related to mosquito ecology and environmental management for malaria control in a rural, agricultural region of Tanzania. Household surveys were conducted with 408 randomly selected respondents from 10 villages and qualitative data were collected through focus group discussions and in-depth interviews. Results show that respondents are well aware of the links between mosquitoes, the environment, and malaria. Most respondents stated that cleaning the environment around the home, clearing vegetation around the home, or draining stagnant water can reduce mosquito populations, and 63% of respondents reported performing at least one of these techniques to protect themselves from malaria. It is clear that many respondents believe that these environmental management practices are effective malaria control methods, but the actual efficacy of these techniques for controlling populations of vectors or reducing malaria prevalence in the varying ecological habitats in Mvomero is unknown. Further research should be conducted to determine the effects of different environmental management practices on both mosquito populations and malaria transmission in this region, and increased participation in effective techniques should be promoted.     

Identifying Malaria Transmission Foci for Elimination Using Human Mobility Data

Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci. By linking transmission to parasite flow, it is possible to stratify landscapes for malaria control and elimination, as sources are disproportionately important to the regional persistence of malaria parasites. Here, we identify putative malaria sources and sinks for pre-elimination Namibia using malaria parasite rate (PR) maps and call data records from mobile phones, using a steady-state analysis of a malaria transmission model to infer where infections most likely occurred. We also examined how the landscape of transmission and burden changed from the pre-elimination setting by comparing the location and extent of predicted pre-elimination transmission foci with modeled incidence for 2009. This comparison suggests that while transmission was spatially focal pre-elimination, the spatial distribution of cases changed as burden declined. The changing spatial distribution of burden could be due to importation, with cases focused around importation hotspots, or due to heterogeneous application of elimination effort. While this framework is an important step towards understanding progressive changes in malaria distribution and the role of subnational transmission dynamics in a policy-relevant way, future work should account for international parasite movement, utilize real time surveillance data, and relax the steady state assumption required by the presented model.     

Seasonally Dependent Relationships between Indicators of Malaria Transmission and Disease Provided by Mathematical Model Simulations

Evaluating the effectiveness of malaria control interventions on the basis of their impact on transmission as well as impact on morbidity and mortality is becoming increasingly important as countries consider pre-elimination and elimination as well as disease control. Data on prevalence and transmission are traditionally obtained through resource-intensive epidemiological and entomological surveys that become difficult as transmission decreases. This work employs mathematical modeling to examine the relationships between malaria indicators allowing more easily measured data, such as routine health systems data on case incidence, to be translated into measures of transmission and other malaria indicators. Simulations of scenarios with different levels of malaria transmission, patterns of seasonality and access to treatment were run with an ensemble of models of malaria epidemiology and within-host dynamics, as part of the OpenMalaria modeling platform. For a given seasonality profile, regression analysis mapped simulation results of malaria indicators, such as annual average entomological inoculation rate, prevalence, incidence of uncomplicated and severe episodes, and mortality, to an expected range of values of any of the other indicators. Results were validated by comparing simulated relationships between indicators with previously published data on these same indicators as observed in malaria endemic areas. These results allow for direct comparisons of malaria transmission intensity estimates made using data collected with different methods on different indicators. They also address key concerns with traditional methods of quantifying transmission in areas of differing transmission intensity and sparse data. Although seasonality of transmission is often ignored in data compilations, the models suggest it can be critically important in determining the relationship between transmission and disease. Application of these models could help public health officials detect changes of disease dynamics in a population and plan and assess the impact of malaria control interventions.     

Inhibition of Malaria Infection in Transgenic Anopheline Mosquitoes Lacking Salivary Gland Cells

Malaria is an important global public health challenge, and is transmitted by anopheline mosquitoes during blood feeding. Mosquito vector control is one of the most effective methods to control malaria, and population replacement with genetically engineered mosquitoes to block its transmission is expected to become a new vector control strategy. The salivary glands are an effective target tissue for the expression of molecules that kill or inactivate malaria parasites. Moreover, salivary gland cells express a large number of molecules that facilitate blood feeding and parasite transmission to hosts. In the present study, we adapted a functional deficiency system in specific tissues by inducing cell death using the mouse Bcl-2-associated X protein (Bax) to the Asian malaria vector mosquito, Anopheles stephensi. We applied this technique to salivary gland cells, and produced a transgenic strain containing extremely low amounts of saliva. Although probing times for feeding on mice were longer in transgenic mosquitoes than in wild-type mosquitoes, transgenic mosquitoes still successfully ingested blood. Transgenic mosquitoes also exhibited a significant reduction in oocyst formation in the midgut in a rodent malaria model. These results indicate that mosquito saliva plays an important role in malaria infection in the midgut of anopheline mosquitoes. The dysfunction in the salivary glands enabled the inhibition of malaria transmission from hosts to mosquito midguts. Therefore, salivary components have potential in the development of new drugs or genetically engineered mosquitoes for malaria control.     

Forcing Versus Feedback: Epidemic Malaria and Monsoon Rains in Northwest India

Malaria epidemics in regions with seasonal windows of transmission can vary greatly in size from year to year. A central question has been whether these interannual cycles are driven by climate, are instead generated by the intrinsic dynamics of the disease, or result from the resonance of these two mechanisms. This corresponds to the more general inverse problem of identifying the respective roles of external forcings vs. internal feedbacks from time series for nonlinear and noisy systems. We propose here a quantitative approach to formally compare rival hypotheses on climate vs. disease dynamics, or external forcings vs. internal feedbacks, that combines dynamical models with recently developed, computational inference methods. The interannual patterns of epidemic malaria are investigated here for desert regions of northwest India, with extensive epidemiological records for Plasmodium falciparum malaria for the past two decades. We formulate a dynamical model of malaria transmission that explicitly incorporates rainfall, and we rely on recent advances on parameter estimation for nonlinear and stochastic dynamical systems based on sequential Monte Carlo methods. Results show a significant effect of rainfall in the inter-annual variability of epidemic malaria that involves a threshold in the disease response. The model exhibits high prediction skill for yearly cases in the malaria transmission season following the monsoonal rains. Consideration of a more complex model with clinical immunity demonstrates the robustness of the findings and suggests a role of infected individuals that lack clinical symptoms as a reservoir for transmission. Our results indicate that the nonlinear dynamics of the disease itself play a role at the seasonal, but not the interannual, time scales. They illustrate the feasibility of forecasting malaria epidemics in desert and semi-arid regions of India based on climate variability. This approach should be applicable to malaria in other locations, to other infectious diseases, and to other nonlinear systems under forcing.     

Can Wolbachia be used to control malaria?

Malaria is a mosquito-borne infectious disease caused by Plasmodium parasites transmitted by the infectious bite of Anopheles mosquitoes. Vector control of malaria has predominantly focused on targeting the adult mosquito through insecticides and bed nets. However, current vector control methods are often not sustainable for long periods so alternative methods are needed. A novel biocontrol approach for mosquito-borne diseases has recently been proposed, it uses maternally inherited endosymbiotic Wolbachia bacteria transinfected into mosquitoes in order to interfere with pathogen transmission. Transinfected Wolbachia strains in Aedes aegypti mosquitoes, the primary vector of dengue fever, directly inhibit pathogen replication, including Plasmodium gallinaceum, and also affect mosquito reproduction to allow Wolbachia to spread through mosquito populations. In addition, transient Wolbachia infections in Anopheles gambiae significantly reduce Plasmodium levels. Here we review the prospects of using a Wolbachia-based approach to reduce human malaria transmission through transinfection of Anopheles mosquitoes.     

Effect of transmission setting and mixed species infections on clinical measures of malaria in Malawi

Background

In malaria endemic regions people are commonly infected with multiple species of malaria parasites but the clinical impact of these Plasmodium co-infections is unclear. Differences in transmission seasonality and transmission intensity between endemic regions have been suggested as important factors in determining the effect of multiple species co-infections.

Principal Findings

In order to investigate the impact of multiple-species infections on clinical measures of malaria we carried out a cross-sectional community survey in Malawi, in 2002. We collected clinical and parasitological data from 2918 participants aged >6 months, and applied a questionnaire to measure malaria morbidity. We examined the effect of transmission seasonality and intensity on fever, history of fever, haemoglobin concentration ([Hb]) and parasite density, by comparing three regions: perennial transmission (PT), high intensity seasonal transmission (HIST) and low intensity seasonal transmission (LIST). These regions were defined using multi-level modelling of PCR prevalence data and spatial and geo-climatic measures. The three Plasmodium species (P. falciparum, P. malariae and P. ovale) were randomly distributed amongst all children but not adults in the LIST and PT regions. Mean parasite density in children was lower in the HIST compared with the other two regions. Mixed species infections had lower mean parasite density compared with single species infections in the PT region. Fever rates were similar between transmission regions and were unaffected by mixed species infections. A history of fever was associated with single species infections but only in the HIST region. Reduced mean [Hb] and increased anaemia was associated with perennial transmission compared to seasonal transmission. Children with mixed species infections had higher [Hb] in the HIST region.

Conclusions

Our study suggests that the interaction of Plasmodium co-infecting species can have protective effects against some clinical outcomes of malaria but that this is dependent on the seasonality and intensity of malaria transmission.     

Evaluating the Performance of Malaria Genetics for Inferring Changes in Transmission Intensity Using Transmission Modeling

Substantial progress has been made globally to control malaria, however there is a growing need for innovative new tools to ensure continued progress. One approach is to harness genetic sequencing and accompanying methodological approaches as have been used in the control of other infectious diseases. However, to utilize these methodologies for malaria, we first need to extend the methods to capture the complex interactions between parasites, human and vector hosts, and environment, which all impact the level of genetic diversity and relatedness of malaria parasites. We develop an individual-based transmission model to simulate malaria parasite genetics parameterized using estimated relationships between complexity of infection and age from five regions in Uganda and Kenya. We predict that cotransmission and superinfection contribute equally to within-host parasite genetic diversity at 11.5% PCR prevalence, above which superinfections dominate. Finally, we characterize the predictive power of six metrics of parasite genetics for detecting changes in transmission intensity, before grouping them in an ensemble statistical model. The model predicted malaria prevalence with a mean absolute error of 0.055. Different assumptions about the availability of sample metadata were considered, with the most accurate predictions of malaria prevalence made when the clinical status and age of sampled individuals is known. Parasite genetics may provide a novel surveillance tool for estimating the prevalence of malaria in areas in which prevalence surveys are not feasible. However, the findings presented here reinforce the need for patient metadata to be recorded and made available within all future attempts to use parasite genetics for surveillance.     

A research agenda for malaria eradication: drugs

Antimalarial drugs will be essential tools at all stages of malaria elimination along the path towards eradication, including the early control or "attack" phase to drive down transmission and the later stages of maintaining interruption of transmission, preventing reintroduction of malaria, and eliminating the last residual foci of infection. Drugs will continue to be used to treat acute malaria illness and prevent complications in vulnerable groups, but better drugs are needed for elimination-specific indications such as mass treatment, curing asymptomatic infections, curing relapsing liver stages, and preventing transmission. The ideal malaria eradication drug is a coformulated drug combination suitable for mass administration that can be administered in a single encounter at infrequent intervals and that results in radical cure of all life cycle stages of all five malaria species infecting humans. Short of this optimal goal, highly desirable drugs might have limitations such as targeting only one or two parasite species, the priorities being Plasmodium falciparum and Plasmodium vivax. The malaria research agenda for eradication should include research aimed at developing such drugs and research to develop situation-specific strategies for using both current and future drugs to interrupt malaria transmission.     

Blockade of TNF receptor 1 reduces disease severity but increases parasite transmission during Plasmodium chabaudi chabaudi infection

Reducing host carriage of transmission-stage malaria parasites (gametocytes) is expected to decrease the population-wide burden of malaria. Some malaria disease severity is attributed to the induction of the pro-inflammatory cytokines TNF-alpha and lymphotoxin-alpha (LT-alpha), and we are interested in whether anti-malaria interventions which ameliorate the symptoms induced by those cytokines may have the capacity to alter malaria transmission. As many functions of TNF-alpha and LT-alpha are exerted through TNF receptor 1 (TNFR1), we investigated the effect TNFR1 blockade exerted on parasite transmission using the rodent malaria Plasmodium chabaudi chabaudi. We found that blocking TNFR1 simultaneously increased gametocyte density and infectivity to mosquitoes, whilst reducing disease severity (weight loss). These transmission-enhancing and severity-reducing effects of TNFR1 blockade were independent of asexual parasite load and were observed for several P. c. chabaudi genotypes. These results suggest that the effects of candidate malaria interventions on infectivity should be examined alongside effects on disease severity so that the epidemiological consequences of such interventions can be evaluated.     

Dynamics of malaria transmission model with sterile mosquitoes

In this paper, a malaria transmission model with sterile mosquitoes is considered. We first formulate a simple SEIR malaria transmission model as our baseline model. Then sterile mosquitoes are introduced into the baseline model. We consider the case that the release rate of sterile mosquitoes is proportional to the wild mosquito population size. To investigate the impact of releasing sterile mosquitoes on the malaria transmission, the dynamics of the baseline model and the models with the sterile mosquitoes are discussed. We derive formulas of the reproductive numbers and explore the existence of endemic equilibrium as the reproductive number is more than unity for these models. It is shown that both the baseline model and the models with the sterile mosquitoes undergo backward bifurcations. Based on theoretical analysis and numerical simulation, we investigate the impact of releasing sterile mosquitoes on malaria transmission.