Abstract
The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the optimal combination of these two control strategies that will minimize the cost of the two control measures and as a result the number of infectious individuals will decrease. We establish the existence for the optimal controls and Pontryagin’s maximum principle is used to characterize the optimal controls. The numerical simulation suggests that optimal control technique is much more effective to minimize the infected individuals and the corresponding cost of the two controls. It is also monitored that in the case of high contact rate, controls have to work for longer period of time to get the desired result. Numerical simulation reveals that the spread of Nipah virus can be controlled effectively if we apply control strategy at early stage.
Highlights
Mathematical modeling has become an important tool for analyzing the spread as well as control of infectious diseases
Since there is no proper vaccination program or appropriate drugs for Nipah Virus (NiV) infections, so in the model we introduce two control strategies, namely, creating awareness (u1) among the community about the risky areas before outbreak of the disease and the treatment (u2)
We monitored the effectiveness of the weight parameter to see how the control is related to weight function. In this simulation we assumed the initial values of S, I and N as proportions instead of whole numbers
Summary
Mathematical modeling has become an important tool for analyzing the spread as well as control of infectious diseases. It is a useful tool for the measurement of the effect of different strategies for controlling the spread of infectious diseases within a population. In recent years epidemiological modeling of infectious disease transmission has had an increasing influence on the theory and practice of disease management and control [1]. How to cite this paper: Sultana, J. and Podder, C.N. (2016) Mathematical Analysis of Nipah Virus Infections Using Optimal Control Theory. N. Podder are a number of different methods for calculating the optimal control for a specific mathematical model. The optimal control strategy is used to minimize the infected individuals and to maximize the total number of recovered individuals
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