Reproduction Ratio Research Articles

Mathematical Modeling of the Co‐Infection Dynamics of Dengue and Malaria Using Delay Differential Equations

AbstractThis study presents a comprehensive mathematical model to analyze the dynamics of co‐infection between dengue and malaria using delay differential equations. The model investigates the transmission dynamics of both diseases, focusing on the stability of equilibrium points and the basic reproductive ratio, which measures the number of secondary infections caused by a single infected individual. A time‐delay component is incorporated to account for the incubation periods, enhancing the model's realism. The study performs a detailed sensitivity analysis and global stability assessments, providing insights into the control and management of diseases. Numerical simulations are conducted to illustrate the effect of various transmission parameters on disease spread. This research highlights the importance of mathematical modeling in understanding co‐infection dynamics and provides critical insights for public health interventions, particularly in regions where both diseases are endemic. The results emphasize the role of controlling transmission rates and the use of vector management strategies in mitigating disease outbreaks.

In Vivo Dynamics of HIV-1 Infection With Impaired Antibody Immunity and Three General Infection Mechanisms

In this paper we investigate two generalized human immunodeficiency virus type-1 (HIV-1) dynamics models with impaired antibody immunity. The models include both latently and actively infected cells. Three infection mechanisms are incorporated into the models, viral infection mechanism (VIM), latent cellular infection mechanism (CIM) and active CIM. The three infection rates are provided by generic nonlinear functions. The second model includes three types of distributed time delays. We find that our models are biologically feasible. The global stability analysis of equilibria are performed and found the basic reproduction ratio (R0) as a threshold parameter. Using Lyapunov method we show that, the virus-free equilibrium is globally asymptotically stable when R0≤1 and the virus-persistence equilibrium is globally asymptotically stable when R0>1. Sensitivity analysis on R0 is studied. To support our theoretical results we provide some numerical simulations. We have demonstrated that R0 is influenced by all three of the infection types, and that if one of them were ignored, R0 would be underestimated. This might lead to inadequate medication effectiveness that aims to remove HIV-1 from the body. The effects of time delay and impaired antibody immunity on HIV-1 progression are examined. According to our research, lowered immunity is a significant factor in the infection's growth. Furthermore, time delays might drastically reduce R0, which would prevent HIV-1 from replicating. The information provided by our research in this work can improve our comprehension of HIV-1 dynamics within-host and provide guidance for the creation of novel pharmacological treatments.

Using the basic reproduction ratio to quantify transmission and identify data gaps for epizootic haemorrhagic disease virus.

Epizootic haemorrhagic disease virus (EHDV) is an arbovirus transmitted by Culicoides biting midges that has recently emerged in Europe. Here, the basic reproduction ratio (R 0) was used to quantify the transmission of EHDV and its dependence on temperature for cattle and deer. Using data from the published literature the parameters needed to calculate R 0 were estimated with Bayesian methods to incorporate uncertainty in the calculations. The Sobol method of sensitivity analysis was used to determine the parameters having the greatest influence on R 0 and, hence, to identify important data gaps. Depending on the strain, the maximum R 0 for EHDV varied from 0.7 to 2.5 in cattle and 1.3 to 4.3 in deer. The maximum R 0 occurred at temperatures between 22 and 25°C, while the lowest temperature at which R 0 exceeded one was between 16 and 20°C. The sensitivity analysis identified the threshold temperature for virus replication, the probability of transmission from host to vector and the vector- to- host ratio as the most important parameters influencing R 0. Furthermore, there are only limited data on EHDV in European deer species and on transmission in wildlife and at the livestock/wildlife interface. These data gaps should be the focus of future research.

A clustered-LPSEIRS malware propagation model in complex networks

In this paper, we present a new malware propagation model that integrates epidemic spread, clustering, and link prediction techniques, tailored for complex network networks. Our model is based on the clustered-link prediction-susceptible-exposed-infected-recovered (clustered-LPSEIRS) epidemic model, which simulates malware dissemination within the network. Our findings reveal a significant decrease in the rate of malware spread compared to the traditional SEIR model, with this enhancement in containment attributed to the integration of clustering and link prediction methods. We also compute the basic reproduction ratio (R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{0}$$\\end{document}) for our model, providing insights into the potential ramifications of malware within the network. By examining parameter variations, we enhance our understanding of the model's behavior under diverse scenarios. Additionally, we assess the influence of clustering and link prediction on mitigating malware spread, emphasizing its effectiveness in diminishing the overall impact.

Mathematical analysis of Ebola considering transmission at treatment centres and survivor relapse using fractal-fractional Caputo derivatives in Uganda

In this article, we seek to formulate a robust mathematical model to study the Ebola disease through fractal-fractional operators. The study thus incorporates the transmission rate in the treatment centers and the relapse rate, since the Ebola virus persists or mostly hides in the immunologically protected sites of survivors. The Ebola virus disease (EVD) is one of the infectious diseases that has recorded a high death rate in countries where it is endemic, and Uganda is not an exception. The world at large has suffered from this deadly disease since 1976 when it was declared epidemic by the World Health Organization. The study employed fractal-fractional operators to identify the epidemiological patterns of EVD, especially in treatment centers and relapse. Memory loss and relapse are mostly observed in EVD survivors and this justifies the use of fractional operators to capture the true dynamics of the disease. Through dynamical analysis, the model is proven to be positive and bounded in the region. The model is further explicitly shown to have a solution that is unique and stable. The reproduction number was duly computed by using the next-generation matrix approach. By taking EVD epidemic cases in Uganda, the study fitted all parameters to real data. It has been shown through sensitivity index analysis that the transmission rate outside treatment centers and relapse have a significant effect on the endemic state of the disease, as they lead to an increase in the basic reproduction ratio.

Modeling of Malware Propagation Under the Clustering Approach in Scale‐Free Networks

ABSTRACTIn this paper, we present an innovative malware propagation model that combines epidemic spread and clustering techniques, specifically designed for scale‐free networks. The proposed model builds upon the susceptible–exposed–infected–recovered (SEIR) framework, effectively simulating the dissemination of malware across the network. Our research demonstrates a notable reduction in the rate of malware transmission compared to the traditional SEIR model, with this improvement in containment being attributed to the incorporation of clustering methodologies. We also calculate the basic reproduction ratio (R0) for the proposed model, which offers valuable insights into the potential consequences of malware outbreaks within the network. By exploring variations in key parameters, we deepen our understanding of the model's behavior under different conditions. Furthermore, we evaluate the role of clustering in mitigating malware spread, highlighting its significant effectiveness in reducing the overall impact of infections.

Modeling of KSHV/HHV-8 and HIV-1 Co-Dynamics in Vivo

Human immunodeficiency virus kind 1 (HIV-1) compromises the immune system by infecting and damaging CD4+ T cells. Infection can progress to the ultimate stage, acquired immune deficiency syndrome (AIDS), if HIV-1 therapy is not received. People living with HIV/AIDS are more vulnerable to infections that they otherwise wouldn’t develop. Opportunistic infections or malignancies are the terms used to describe them. Kaposi sarcoma (KS) is an AIDSrelated malignancy caused by Kaposi’s sarcoma-associated herpesvirus (KSHV) (also known as human herpesvirus 8 (HHV-8)). HIV-1 and KSHV co-infection cases has been shown in several studies. Using a system of ODEs, we develop a new mathematical model to study the co-dynamics of HIV-1 and KSHV in vivo. The model includes interactions between healthy CD4+ T cells, HIV-1-infected CD4+ T cells, HIV-1 particles, healthy B cells, KSHV-infected B cells, and KSHV particles. By analyzing the boundedness and nonnegativity of the solutions, we prove the mathematical well-posedness and biological compatibility of the model. The existence and stability of the model’s steady states are established by four threshold values that we identify. We prove that steady states are globally asymptotically stable by using Lyapunov’s method and LaSalle’s invariance principle. Numerical simulations are used to display the results. For both basic reproduction ratios of HIV-1 mono-infection (R1) and KSHV mono-infection (R2), sensitivity analysis is carried out. A comparison between HIV-1 or KSHV mono-infections and co-infections with HIV-1 and KSHV is given. Empirical evidence indicates that co-infection results in higher KSHV and HIV-1 concentrations compared to mono-infection cases. This result is in line with a number of findings found in the literature.

Toxicity and fitness evaluation of Chrysoperla carnea resistant strains on cotton mealy bug Phenacoccus solenopsis Tinsely

Research was conducted to select chlorantraniliprole and bifenthrin resistant strains of Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae) at Bahauddin Zakariya University, Multan, Pakistan. Moreover, fitness parameters of resistant C. carnea were evaluated after feeding on 2nd instars nymph of Phenacoccus solenopsis Tinsley (Hemiptera: Pseudococcidae). Two to three day old C. carnea larvae were used in each topical bioassay. The raw data of biological parameters were analysed using an age stage, two sex life table. After 16 and 13 rounds of selection, the Chlo-Sel and Bife-Sel strains of C. carnea developed 91- and 2.19-fold resistance level, respectively compared with the UN-Sel strain. Biological parameters such as larval duration (days), pupal duration (days), female longevity (days), male longevity (days), adult pre-oviposition period (APOP) (days), total pre-oviposition period (TPOP) (days), oviposition (days), reproductive female ratio (RepF/Fn), and fecundity/female (F) were significantly different while pre-adult female (days), pre-adult male (days), and female ratio (Nf/N) was not significantly different among all strains. Demographic parameters such as finite rate of increase (λ), mean generation time (T), intrinsic rate of increase (r), net reproductive rate (Ro), and gross reproductive rate (GRR) were significantly different while doubling time (DT) was significantly similar among all strains of C. carnea. This information could be helpful in developing and promoting the use of insecticide resistant strains of C. carnea for the management of P. solenopsis under field conditions. Moreover, knowledge of fitness advantages will be helpful in IPM for the development of control strategies against P. solenopsis. In order to explore the practical relevance of our findings, more research ought to be conducted.

Revisiting the risk of introduction of Japanese encephalitis virus (JEV) into the United States – An updated semi-quantitative risk assessment

Japanese encephalitis virus (JEV) is associated with encephalitis in humans and reproductive and neurological illness in pigs. JEV has expanded beyond its native distribution in southeast Asia, with identifications in Europe (2010) and Africa (2016), and most recently, its spread into mainland Australia (2021−2022). The introduction of JEV into the United States (US) is a public health risk, and could also impact animal health and the food supply. To efficiently and cost-effectively manage risk, a better understanding of how and where diseases will be introduced, transmitted, and spread is required. To achieve this objective, we updated our group's previous qualitative risk assessment using an established semi-quantitative risk assessment tool (MINTRISK) to compare the overall rate of introduction and risk, including impacts, of JEV in seven US regions. The rate of introduction from the current region of distribution was considered negligible for the Northeast, Midwest, Rocky Mountain, West, Alaska, and Hawaii regions. The South region was the only region with a pathway that had a non-negligible rate of introduction; infected mosquito eggs and larvae introduced via imported used tires (very low; 95% uncertainty interval (UI) = negligible to high). The overall risk estimate for the South was very high (95% UI = very low to very high). Based on this risk assessment, the South region should be prioritized for surveillance activities to ensure the early detection of JEV. The assumptions used in this risk assessment, due to the lack of information about the global movement of mosquitoes, number of feral pigs in the US, the role of non-ardeid wild birds in transmission, and the magnitude of the basic reproduction ratio of JEV in a novel region, need to be fully considered as these impact the estimated probability of establishment.

Stability of generalized models for HIV-1 dynamics with impaired CTL immunity and three pathways of infection

Highly active antiretroviral therapy (HAART) stands out as the most effective treatment for human immunodeficiency virus type-1 (HIV-1). While total eradication is still difficult, HAART can dramatically lower the virus's plasma viral level below the detection threshold. The activation of latently infected cells is considered to be the main obstacle to the total eradication of HIV-1 infection. This study investigates the dynamic characteristics of two generalized HIV-1 infection models taking into account the impairment of cytotoxic T lymphocytes (CTLs). These models include CD4+T cells that are latently infected and equipped with the capability to engage in cell-to-cell infection and elude immune responses. We introduce models featuring three infection pathways: virus-to-cell (VTC), latent cell-to-cell (L-CTC), and active cell-to-cell (A-CTC). The three pathways' infection rates are characterized by general functions, which cover the many types of infection rates documented in the literature. The second model integrates three distinct types of distributed-time delays. We demonstrate the validity of the suggested models, through their well-posedness. We determine the basic reproduction ratio (ℜ0) of the systems. Lyapunov functions and LaSalle's invariance principle are employed to verify that the global stability of both the virus-free steady state (O0) and the virus-persistence steady state (O1). More precisely, O0 achieves global asymptotic stability when ℜ0 ≤ 1, whereas O1 attains global asymptotic stability when ℜ0 > 1. To demonstrate the impact of the parameter values on ℜ0, we examine the sensitivity analysis. It is illustrated that ℜ0 comprises three components, namely ℜ0E, ℜ0P, and ℜ0K, corresponding to the transmissions of VTC, L-CTC, and A-CTC, respectively. Thus, if the L-CTC pathway is disregarded in the HIV-1 infection model, ℜ0 may be underestimated, which could lead to inadequate or erroneous medication therapy focused on eradicating HIV-1 within the body. To demonstrate the associated mathematical outcomes, we conduct numerical simulations through an illustrative example. Specifically, we delve into how the dynamics of HIV-1 are influenced by both immune impairment and time delay. Our findings suggest a significant role of reduced immunity in the progression of the infection. Furthermore, time delays possess the potential to markedly reduce ℜ0, thereby impeding the replication of HIV-1.

Engineered deletions of HIV replicate conditionally to reduce disease in nonhuman primates.

Antiviral therapies with reduced frequencies of administration and high barriers to resistance remain a major goal. For HIV, theories have proposed that viral-deletion variants, which conditionally replicate with a basic reproductive ratio [R0] > 1 (termed "therapeutic interfering particles" or "TIPs"), could parasitize wild-type virus to constitute single-administration, escape-resistant antiviral therapies. We report the engineering of a TIP that, in rhesus macaques, reduces viremia of a highly pathogenic model of HIV by >3log10 following a single intravenous injection. Animal lifespan was significantly extended, TIPs conditionally replicated and were continually detected for >6 months, and sequencing data showed no evidence of viral escape. A single TIP injection also suppressed virus replication in humanized mice and cells from persons living with HIV. These data provide proof of concept for a potential new class of single-administration antiviral therapies.

Bovine leukemia virus transmission rates in persistent lymphocytotic infected dairy cows.

Bovine leukemia virus (BLV) establishes a lifelong persistent infection in dairy cattle. White blood cell count (WBC) is correlated with proviral load in the blood and milk of BLV-infected cattle, and testing WBC can be used to assess both BLV infectiousness levels and risk of BLV transmission from different types of infected animals. The objective of the study was to compare effective transmission rates (β) and the basic reproduction ratio (R o) among two types of BLV-infected dairy cows in Chile: those affected with persistent lymphocytosis (PL) vs. aleukemic (AL).The estimated (β) coefficient was higher in PL cattle [1.1; 95% Confidence interval (CI) (-1.6, 3.8)], compared to AL cattle (-3.1; 95% CI = -3.7, -2.5). In addition, the R o was higher in PL cattle (60.4; 95% CI = 3.5; 820.6), compared to AL cattle (1.5; 95% CI = 0.7, 3.1). The ratio between PL/AL expected rate of cases was 73.9. The estimated effective transmission rate and the Ro were higher in PL cattle compared to AL cattle. The WBC test is a convenient alternative that can be considered for risk identification and risk management of BLV infection in dairy herds; particularly in livestock regions where laboratory capacity is limited (e.g., use of PCR or gene sequencing techniques) and/or molecular tests are not cost-effective. Therefore, when prevalence of infection is high, the removal of PL cattle should be engaged to control BLV within-herds.

Vine spacing of <i>Vitis vinifera</i> cv. Shiraz/101-14 Mgt. III. Grape and wine quality

Vine spacing effects of Shiraz/101-14 Mgt on a relatively high potential soil in the Breede River Valley, Robertson, South Africa, on grape composition and wine quality, were investigated. Canopies were VSP trellised and orientated approximately NNE-SSW. Spacing between rows was fixed at 2.2 m. In-row vine spacing changed from 0.3 – 4.5 m with increments of 30 cm (from 15151 – 1010 vines/ha). Grape composition and wine quality were monitored over six seasons and two grape ripeness levels. Decreasing trends of soluble solids (°B) and pH and increasing titratable acidity from narrow to wide spacing were observed. Sugar accumulation of wider spacings seemed delayed. Berry skin total anthocyanin index and phenol content showed virtually no change. Malvidin mono-glucoside and its p-coumaroyl and acetyl derivatives were present in the highest concentrations, followed by peonidin-, petunidin-, delphinidin- and cyanidin mono-glucosides and derivatives, each vine spacing treatment displaying a unique grape anthocyanin profile. The narrower spacing of vines seemed to favour skin anthocyanin accumulation compared to wider spacing. Decreasing trends in wine total anthocyanin intensity, anthocyanin density, and phenols were observed from narrow to wide spacing; all had higher levels in wines from riper grapes. Individual wine anthocyanin concentrations also showed qualitative profile changes. The first regression join points for all anthocyanins occurred around 1.8 – 2.4 m vine spacing; those for malvidin and derivatives consistently appeared at 1.8 m spacing. Although volatile compounds only seemed to respond to ripeness level and not to vine spacing, wine sensory quality generally decreased with wider vine spacing at both grape ripeness levels. Given the changes in biotic and abiotic growth conditions with wider vine spacing, the results likely displayed adaptation to the combined impact of increasing light exposure, berry temperature, physiological functioning, vegetative and reproductive growth ratios, and plant stress. The study showed the prominent role of plant spacing in sustainable grape growing and wine outcomes and thus the importance of judicious decision-making during the establishment and management of vines under any growth conditions and in any terroir.

A mathematical model for a disease outbreak considering waning-immunity class with nonlinear incidence and recovery rates

In the spread of infectious diseases, intervention levels play a crucial role in shaping interactions between healthy and infected individuals, leading to a nonlinear transmission process. Additionally, the availability of medical resources limits the recovery rate of infected patients, adding further nonlinear dynamics to the healing process. Our research introduces novelty by combining nonlinear incidence and recovery rates alongside waning immunity in an epidemic model. We present a modified SIRW-type model, examining the epidemic problem with these factors. Through analysis, we explore conditions for non-endemic and co-existing cases based on the basic reproduction ratio. The local stability of equilibria is verified using the Routh-Hurwitz criteria, while global stability is assessed using Lyapunov functions for each equilibrium. Furthermore, we investigate bifurcations around both non-endemic and co-existing equilibria. Numerically, we give some simulations to support our analytical findings.

A holistic exploration of the optimal control strategies on an enhanced mathematical model for the co-infection of HIV/AIDS and varicella-zoster

Because of its high contagiousness and correlation with HIV/AIDS complaints, the virus that causes varicella-zoster virus and its interactions have major consequences for a considerable portion of people worldwide. The primary aim of this work is to suggest and examine optimal control methods for managing the transmission dynamics of HIV/AIDS and Varicella-Zoster co-infection, using an integer model approach. The mathematical analyses of the proposed integer order model places particular emphases on the boundedness and non-negativity of the model solutions, scrutinizing equilibrium points, determining the models basic reproduction ratios (the models basic reproduction numbers) through the next-generation matrix operator method, and assessing the model equilibrium points existences and stabilities in local approach by considering the local stability conditions of Routh and Hurwitz. Additionally, it incorporates an optimal control framework to enhance our understanding of the dynamics involved in the spreading of HIV/AIDS and Varicella-Zoster co-infection within a considered population. This entails determining preventative measures that can be deliberately put into place to lessen the effects of these co-infections. The solutions of the HIV/AIDS and Varicella-Zoster co-infection model converges to the co-infection endemic equilibrium point whenever the associated basic reproduction number is greater than unity, as verified by numerical simulation results. Including optimal management gives the research an innovative viewpoint and helps identify tactical ways to mitigate the negative effects of this co-infection on the public health. The results highlight how crucial it is to address these complex structures in order to protect and improve public health outcomes. Implementing the proposed protection measures and treatment measures simultaneously has most effective result to minimize and eliminate the HIV/AIDS and Varicella-Zoster co-infection disease throughout the population.

Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations

Estimates of the reproduction ratio from epidemic surveillance may be biased in spatially structured populations

Dynamics of HIV-1 and HTLV-1 Coinfection with both CTL and Antibody Responses

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type 1 (HTLV-1) coinfection models with simply an antibody response or a CTL response have been the subject of several recent investigations. Thus, the primary objective of this paper is to formulate and examine a mathematical framework for analyzing the intricate dynamics of coinfection between HIV-1 and HTLV-1. The model takes into account the role of antibody response against free HIV-1 particles and CTL response against HTLV-1-infected cells. We prove that the model is well-posed and it admits eight equilibria. The stability and existence of the equilibria are precisely controlled by eight threshold parameters ℜi, i = 1, 2, ..., 8. By formulating suitable Lyapunov functions and applying LaSalle's invariance principle, we show the global asymptotic stability for all equilibria. To demonstrate the theoretical results, we conduct numerical simulations. We look at how the antibody and CTL responses affect the dynamical behavior of HIV-1/HTLV-1 coinfection. Although the parameters of antibody and CTL responses have no effect on the basic reproduction ratio of HIV-1 single-infection (ℜ₁) and HTLV-1 single-infection (ℜ₂), it has been demonstrated that viral coinfection can be inhibited by immunological activation of antibody and CTL responses. This could potentially facilitate the advancement of therapeutic approaches for HIV-1 and HTLV-1, which have the capability to enhance the HIV-1-specific antibody and HTLV-1-specific CTL reactions.

Interconnected Takagi-Sugeno system and fractional SIRS malware propagation model for stabilization of Wireless Sensor Networks

This paper is devoted to investigate the dynamical behaviors of malware attack on a familiar kind of complex heterogeneous networks, namely Wireless Sensor Network, and discuss an effective immunization treatment based on fractional interconnected Takagi-Sugeno (T-S) fuzzy systems. Our approach is based on the mathematical modeling to establish a controlled fractional network-based SIRS malware propagation model that better describes the attacking behavior of malicious objects on Wireless Sensor Network. After that, we point out some qualitative properties of the proposed network-based SIRS malware propagation model such as the existence of positively invariant set, backward bifurcation and asymptotic behavior. Especially, in order to study the model's stability, we evaluate an epidemiological threshold value R0, namely basic reproductive ratio, which ensures the existence of at least one endemic equilibrium P⁎ and the local asymptotic stability of malware-free equilibrium P0. As a consequence of theoretical result, the malware-free equilibrium P0 is unstable when R0>1 and hence, the rest of this paper is to address a stabilization problem for the proposed controlled network-based model and establish some sufficient conditions related to linear matrix inequalities and positive definite matrices. Finally, we illustrate the obtained theoretical results by a computational example.

Global Sensitivity Analysis of A Rabies Epidemic Model involving Dog Vaccination and Dog Population Management

Rabies is a zoonotic disease which is spread by animals mostly carnivores. Rabies regards as tropic disease. In this article, we construct a mathematical model for rabies involving dog vaccination and dog population management. The model has two equilibrium points, namely rabies-free equilibrium point and endemic equilibrium point. We determine the effective reproduction ratio using next generation matrix. Our dynamical analysis shows that rabies-free equilibrium point is conditionally stable. A global sensitivity analysis is performed to investigate which intervention is the most crucial among the two interventions considered in the model. We use Latin hypercube sampling method to generate parameter space. To investigate the parameter sensitivity, we calculate the partial rank correlation coefficient. We provide numerical experimental results related to stability and global sensitivity analysis. Our results show that the effective reproduction ratio is more sensitive to dog population management than vaccination intervention. This suggests that dog population management intervention, such as sterilization and monitoring of dog movements significantly reduces the effective reproduction ratio compared to vaccination programs. In addition, the number of infectious dogs has a strong correlation with dog culling actions.

An analytically tractable, age-structured model of the impact of vector control on mosquito-transmitted infections.

Vector control is a vital tool utilised by malaria control and elimination programmes worldwide, and as such it is important that we can accurately quantify the expected public health impact of these methods. There are very few previous models that consider vector-control-induced changes in the age-structure of the vector population and the resulting impact on transmission. We analytically derive the steady-state solution of a novel age-structured deterministic compartmental model describing the mosquito feeding cycle, with mosquito age represented discretely by parity-the number of cycles (or successful bloodmeals) completed. Our key model output comprises an explicit, analytically tractable solution that can be used to directly quantify key transmission statistics, such as the effective reproductive ratio under control, Rc, and investigate the age-structured impact of vector control. Application of this model reinforces current knowledge that adult-acting interventions, such as indoor residual spraying of insecticides (IRS) or long-lasting insecticidal nets (LLINs), can be highly effective at reducing transmission, due to the dual effects of repelling and killing mosquitoes. We also demonstrate how larval measures can be implemented in addition to adult-acting measures to reduce Rc and mitigate the impact of waning insecticidal efficacy, as well as how mid-ranges of LLIN coverage are likely to experience the largest effect of reduced net integrity on transmission. We conclude that whilst well-maintained adult-acting vector control measures are substantially more effective than larval-based interventions, incorporating larval control in existing LLIN or IRS programmes could substantially reduce transmission and help mitigate any waning effects of adult-acting measures.