Optimal control and cost-effective analysis of malaria/visceral leishmaniasis co-infection

Abstract

In this paper, a deterministic model involving the transmission dynamics of malaria/visceral leishmaniasis co-infection is presented and studied. Optimal control theory is then applied to investigate the optimal strategies for curtailing the spread of the diseases using the use of personal protection, indoor residual spraying and culling of infected reservoirs as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And we investigated the most cost-effective strategy of all the control strategies using three approaches, the infection averted ratio (IAR), the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER). Our results show that the implementation of the strategy combining all the time dependent control variables is the most cost-effective control strategy. This result is further emphasized by using the results obtained from the cost objective functional, the ACER, and the ICER.

Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

“…Then substituting expressions (22) and (25) into the equation in (23) and simplifying lead to the following quadratic equation:…”

“…In [18,20,22,25], global stability of equilibria has been investigated using suitable Lyapunov functions; and their results show that the disease-free and endemic equilibrium points become globally asymptotically stable if 0 ≤ 1 and 0 > 1, respectively. Application of the optimal control theory becomes an important tool for investigating the efficiency of joint control intervention strategies to minimize the impact of malaria disease and cost-effectiveness of implementing them [19,21,23,24]. Their studies suggest that the optimal control strategies can effectively reduce the malaria disease.…”

Implicit versus explicit control strategies in models for vector-borne disease epidemiology

“…Optimal control theory provides a set of mathematical tools which, when applied to vector-borne disease models, can be used to find control protocols for achieving a control objective, such as R 0 < 1, which minimizes a cost of control, or to find control protocols which optimally balance a disease cost with a cost of control. Typically, for human intervention strategies, the cost of control is taken to be a monetary cost associated with control implementation, and modeling results in this regard can be of great utility for informing public policy decisions subject to budgetary constraints [2,3,4,5,12,14,16,25,26,42].…”

“…To assess the effects and efficacy of real-world vector management strategies using a mathematical model, a modeler must first select a scheme by which the control's influence will be incorporated into the model's structure or behavior. One common choice is to simply infer the effects of control by analyzing changes in model behavior under variations in model parameters relative to their natural values [2,4,5,6,9,12,13,14,15,16,17,18,19]. For example, in many vector-borne disease models, the effects of adulticide on outbreak severity are inferred through the responses of important threshold quantities like the basic reproduction number [20,21] to increases in vector death rates, while the effects of larvicides are inferred through the analogous responses to increases in larval death rates or decreases in vector emergence rates [14,15,17,18].…”

Optimal Control of Rumor Spreading Model with Consideration of Psychological Factors and Time Delay

“…A number of studies introduce vaccination and treatment on the spread of infectious diseases by using the control theory [26][27][28]. Due to the high similarity between rumor spreading model and epidemic model, various optimal control models were also proposed in rumor model.…”