Transmission Dynamics and Optimal Control of Malaria-Dengue Co-infection: A Cost-Effectiveness Analysis

Optimal Control Analysis and Cost – Effectiveness of Dengue Transmission Model Along With Implementation Time Effects in Applying the Control Interventions

Dengue fever poses a significant global public health threat, and its effective management requires a comprehensive approach to control the dengue prevalence. This study proposes an optimal control problem for the dengue transmission, incorporating three key control measures: information‐induced self‐protection, saturated treatment, and pesticide use for vector control, and is analyzed using Pontryagin's Maximum Principle. Importantly, a novel higher nonlinearity in the cost construction is incorporated. Seven distinct control policies ( P1−P7$$ {P}_1-{P}_7 $$ ) incorporating different combinations of control measures are designed and evaluated through numerical simulations. The results demonstrate that the combined strategy of all controls (Policy P7$$ {P}_7 $$ ) is the most effective, reducing infection prevalence to minimal levels within approximately 60 days, while maintaining sustained control thereafter. In comparison, the combined use of information and treatment (Policy P4$$ {P}_4 $$ ) achieves a similar outcome but requires nearly 120 days to stabilize the infection. Among single‐control strategies, information‐induced self‐protection (Policy P1$$ {P}_1 $$ ) outperforms treatment ( P2$$ {P}_2 $$ ) and pesticide application ( P3$$ {P}_3 $$ ) when applied alone. Cost‐effectiveness analysis using CCER, IAR, and ICER reveals that Policy P1$$ {P}_1 $$ is the most cost‐effective intervention, with the lowest CCER value, while Policy P7$$ {P}_7 $$ averts the highest number of infections. Furthermore, the analysis shows that the control's effectiveness depends strongly on epidemic severity: for mild outbreaks ( R0≤2.5$$ {R}_0\le 2.5 $$ ), combined strategies such as P4$$ {P}_4 $$ and P6$$ {P}_6 $$ (treatment and pesticide) perform efficiently, whereas for severe outbreaks ( R0>2.5$$ {R}_0>2.5 $$ ), comprehensive control ( P7$$ {P}_7 $$ ) becomes essential. Additionally, delayed implementation of control measures significantly worsens disease outcomes, increasing infection peaks and economic burden. Overall, the study highlights the importance of timely and integrated intervention strategies and provides quantitative insights for optimal resource allocation in dengue control.

Optimal control approach to developing sex-structured release strategies for dengue prevention.

Dengue remains a public health challenge due to the persistence of Aedes aegypti populations and the limited effectiveness of medical and vector control interventions. The release of Wolbachia-infected mosquitoes has been used in multiple regions; yet, release protocols are often heuristically structured, with limited optimization. In particular, the impacts of mosquito sex structure and strain-specific effects remain unclear. This study develops a sex-structured dynamical model that links within-vector Wolbachia dynamics, such as cytoplasmic incompatibility and vertical transmission, with between-host dengue transmission. An optimal control framework is used to determine cost-effective releases of male and female mosquitoes over a finite intervention horizon, with mosquito dispersal on a finite time interval. The cost effectiveness of a release program relies on minimizing releases and dengue cases. The approach is applied to three Wolbachia strains, wAlbB, wMel, and wMelPop, to assess how strain-specific fitness and viral blocking influence optimal release plans. The analysis identified sex-structured strategies that diverge from in-field protocols, supporting the notion that commonly used plans may benefit from optimization by sex. Additionally, differences were noted among strains, which suggests that optimal sex-structured releases may vary with Wolbachia strain used.

Impact of Four-Dose Vaccination on the Transmission Dynamics of a Fractional-Order Malaria Model in the Context of Sub-Saharan Africa

This study develops a comprehensive mathematical framework for analyzing the transmission dynamics of malaria, with particular emphasis on a four-dose vaccination strategy combined with treatment interventions as primary control mechanisms. The model stratifies the human population into nine compartments—susceptible, exposed, infected, under treatment, recovered, and four sequential vaccination classes (V 1 through V 4 )—together with susceptible and infected vector populations, all governed by a system of ordinary differential equations. Analysis of the diseasefree equilibrium demonstrates local asymptotic stability when the basic reproduction number R 0 < 1, while a unique endemic equilibrium exists and is stable when R 0 > 1. Sensitivity analysis identifies the mosquito biting rate, transmission probability, first-dose vaccination rate, and treatment rate as the most influential parameters governing malaria dynamics. Numerical simulations confirm that increasing vaccination coverage and completion rates across all four doses, in conjunction with optimized treatment, substantially reduces malaria incidence. To capture long-term memory effects inherent in malaria transmission—particularly non-exponential immunity waning and heterogeneous parasite development—a Caputo fractional-order version of the model is introduced, solved using the Adams–Bashforth predictor-corrector method. Comparison of the integer-order and fractional-order results reveals that memory effects slow the approach to equilibrium and may lead to higher endemic levels under identical intervention parameters, underscoring the value of the fractional extension. These findings emphasize that achieving high completion rates across all four vaccination doses, sustained treatment access, and integrated vector control are essential for meaningful progress toward malaria elimination in Sub- Saharan Africa.

Optimal control strategies for dengue transmission under varying adult prevalence of Wolbachia-carrying mosquitoes: a deterministic mathematical modeling study.

Objectives This study aimed to develop prevalence-informed post-release dengue control strategies for settings in which Wolbachia-carrying Aedes aegypti mosquitoes have become established through population replacement and to quantify how optimal supplementary intervention intensity and duration vary with adult Wolbachia prevalence, pW. Methods A deterministic human-mosquito model was formulated that included Wolbachia-free and Wolbachia-carrying mosquitoes and incorporated cytoplasmic incompatibility, maternal transmission, and reduced vector competence. Two bounded supplementary controls were optimized over a 3-year horizon: reduction of effective human-mosquito contact and conventional adult mosquito suppression, represented by increased adult mortality. A quadratic-cost optimal-control problem was solved numerically using the Pontryagin maximum principle and a forward/backward sweep algorithm. Outcomes were compared across representative pW scenarios and prevalence scans. Results The optimal policies applied high-intensity supplementary control early in the planning horizon and then relaxed control as infection pressure declined. Higher pW reduced the uncontrolled infection burden, decreased the incremental benefit of additional intervention, and shortened the duration of maximum control. In coarse scans with umax=0.30, the terminal dengue infection near-elimination indicator, defined as IH (T)≤10-4 at T=3 years, changed between pW=0.45 and pW=0.50 for all tested cost-weight combinations. A separate refined continuation example demonstrated non-monotonic mean control use and a sharp decrease in cumulative incidence. Conclusion Adult Wolbachia prevalence measured through entomological surveillance may represent an actionable index for post-release dengue management. The identified transition band is a model-based planning indicator, not a universal field threshold or evidence of mosquito population elimination.

Mathematical Analysis and Optimal Control of a Tuberculosis Model with Early Diagnosed Latent Infections

Tuberculosis (TB) remains one of the most dangerous infections disease and a major public health problem. This study develops an SEIR model for TB transmission, taking into account the early diagnosed latent infections. The model is used to derive the basic reproductive number \(\mathcal{R}_0\), study equilibrium points, and identify the most influential parameters through sensitivity analysis on \(\mathcal{R}_0\). An optimal control is formulated using four interventions: transmission reduction, early diagnosed latent TB, treatment, and vaccination. Different strategies are compared using infection averted, total cost, the average cost effectiveness ratio (ACER) and incremental cost effectiveness ratio (ICER). The results show that combined strategy which involve all interventions reduce the total cost, while transmission reduction only strategy gives the greatest reduction in infected individuals.

Mathematical Modelling of Tuberculosis Transmission Dynamics and Optimal Control in Nairobi, Kenya: An SEIR Compartmental Analysis